That is probably a question that wants to be standalone. I will answer it here for now but might split it later.
Yes, no, possibly and "it depends" is the answer there, and for various reasons some might even opt to backport a script to another version (European language to European language is usually not so bad as European to Japanese).
In normal infinite money/ammo/items/stats/character party members/... cheats then you can't assume a simple offset, in many cases it could well be but it is not the whole story.
Now in a lot of cases having a known cheat means you can look at the game, find either a fixed set of data nearby or something more obvious (why spend 10 hours upgrading luck in the average RPG to do searches with if you can change attack in 10 seconds and move sideways) and probably also be reasonably sure you have the same format which itself could be something hard fought to find*; give or take easy mode-hard mode coming out of Japan in 16 bit and older games then most games will use the same numbers, mainly being weights and other "real world" measurements that get changed, and even then it is many times it is a conversion or someone just swaps the terms out (yards is near enough metres for most purposes in games, and while it can get a bit more radical to have your pokemon measured in kilograms from pounds then... eh). The troubles mostly come from names (we tend to see similar things in converting saves between regions) where Japanese 16 bit encoding (one of the major problems backporting to a Japanese base or vice versa) means data all ends up shuffled around that little bit to account for it for all the character/weapon/party member/... names a player might enter over the course of a game that might not all come at once in a big data block.
*so you have a timer in the game that times you out after 10 minutes but counts up on screen. Not knowing whether it counts up, counts down from a value (subtraction is annoying to do vs addition every frame or something, especially in older systems, so the time on screen might be converted to a human number and doing the opposite to the internal clock which is far easier to handle), counts in frames, counts in milliseconds, counts in hundreths, counts in something else entirely. Similar things can happen in anything, or be fairly obvious but have a valid range it has to stick to lest it crash and the cheat might reflect that (8 bits might support 255 but give yourself 255 potions and watch the game crash, instead stick with 99).
Widescreen cheats are however a rather different matter to normal cheats.
There are four approaches seen in such things.
1) Internal hardware change. This can also be region specific (the PAL xbox for instance not natively supporting high res options, though you can hack them to, see enigmah video mode switcher) and PAL usually gets the short end of the stick for this one and lacks the fun stuff. Could well see a cheat enable it though, possibly even a fairly universal one (if it is a fixed location in hardware that needs to be twiddled, possibly one the average cheat like you have there is there to alter the game's code to do itself**) that a lua cheat like this could do happily.
2) Internal software change. More modern systems (though N64*** is not necessarily modern) might be able to do things at a software level and thus be able to be tweaked by cheats. This might also be something lost when converted to PAL (most systems that have a sensible resolution change option here are compiled code which means anything pointless and just going to take memory up might well get lost by the compiler rather than ignored for the sake of not having to do more work like 16 bit and older might have been) or changed radically such that you need a new cheat.
Some things might define a resolution you want to change, some might have it as a mode you can select/force by a cheat (if 0, if 1, if 2... works just the same as text speed up, flag based cheats like no monsters courtesy of potion, this button combo on title screen forces different language sorts of cheats, here you presumably playing on whatever selection menu the game provides and then possibly trying numbers outside what it gives you by normal menu options).
3) Cropping aka letterboxing. I don't know whether to hunt these people down first or those that stretch images not meant to be stretched (that is an option if the original devs make the textures designed to be stretched and look correct once they are, you lose some detail but hey). Not normally something I would expect to be seen done by cheats though, however it could be an internal option.
4) Emulator style camera rendering, though can be seen in hardware (the DS widescreen hacks for 3ds custom firmware users for instance, similar things also existing for GC games on the Wii). Here most things have an entire 3d world in memory and thus you can tweak the camera a bit to render a bit more of it. Some of these need cheats to also change some things (enemies might only move at the "side" of the screen which is now however many degrees in), if https://www.widescreengamingforum.com/wiki/index.php/Main_Page is anything to go by then you might need field of view, you might need to change the UI (some effects, UI elements and more are 2d images overlaid onto things which means your nice blurry/shadow lens effect is lost at the edges). There is also the emulator style take a savestate every frame, force the camera/player character (possibly disabling random battles and adding a noclip mode) to move either every direction (higher res) or left-right (widescreen, unless it is a vertical shmup in which case up-down might be the case unless you consider that it is probably just actually a TV on its side and...) and stitch it all together, other than those specific things that might do a wall walk and battle disable cheat then that is not really relevant in this.
**most conventional cheat engines, cartridges and the like often struggle to alter anything other than the basic RAM a console has with anything more specialist (which video aspects tend to fall under) in the hardware itself being off limits, that is until you realise the code (likely sitting in RAM for anything you are doing a widescreen cheat for and CD read speeds and latencies are brutal when your CPU is measured in hundreds of megahertz, if not gigahertz) can do it happily and thus change that to in turn change the normally inaccessible area. This then is closer to the more classical convert a gameshark/action replay/codebreaker/goldfinger/... code (AKA RAM code) to game genie (AKA ROM code, or for some reason assembly cheat in Switch hacking circles).
***video covering a few things here for N64 expansion pack, many of which I could see be activated by a very simple cheat (even those things not already gated behind a cheat in the "go here and enter this password/do a bit of finger wizardry on the menu).
Yes, no, possibly and "it depends" is the answer there, and for various reasons some might even opt to backport a script to another version (European language to European language is usually not so bad as European to Japanese).
In normal infinite money/ammo/items/stats/character party members/... cheats then you can't assume a simple offset, in many cases it could well be but it is not the whole story.
Now in a lot of cases having a known cheat means you can look at the game, find either a fixed set of data nearby or something more obvious (why spend 10 hours upgrading luck in the average RPG to do searches with if you can change attack in 10 seconds and move sideways) and probably also be reasonably sure you have the same format which itself could be something hard fought to find*; give or take easy mode-hard mode coming out of Japan in 16 bit and older games then most games will use the same numbers, mainly being weights and other "real world" measurements that get changed, and even then it is many times it is a conversion or someone just swaps the terms out (yards is near enough metres for most purposes in games, and while it can get a bit more radical to have your pokemon measured in kilograms from pounds then... eh). The troubles mostly come from names (we tend to see similar things in converting saves between regions) where Japanese 16 bit encoding (one of the major problems backporting to a Japanese base or vice versa) means data all ends up shuffled around that little bit to account for it for all the character/weapon/party member/... names a player might enter over the course of a game that might not all come at once in a big data block.
*so you have a timer in the game that times you out after 10 minutes but counts up on screen. Not knowing whether it counts up, counts down from a value (subtraction is annoying to do vs addition every frame or something, especially in older systems, so the time on screen might be converted to a human number and doing the opposite to the internal clock which is far easier to handle), counts in frames, counts in milliseconds, counts in hundreths, counts in something else entirely. Similar things can happen in anything, or be fairly obvious but have a valid range it has to stick to lest it crash and the cheat might reflect that (8 bits might support 255 but give yourself 255 potions and watch the game crash, instead stick with 99).
Widescreen cheats are however a rather different matter to normal cheats.
There are four approaches seen in such things.
1) Internal hardware change. This can also be region specific (the PAL xbox for instance not natively supporting high res options, though you can hack them to, see enigmah video mode switcher) and PAL usually gets the short end of the stick for this one and lacks the fun stuff. Could well see a cheat enable it though, possibly even a fairly universal one (if it is a fixed location in hardware that needs to be twiddled, possibly one the average cheat like you have there is there to alter the game's code to do itself**) that a lua cheat like this could do happily.
2) Internal software change. More modern systems (though N64*** is not necessarily modern) might be able to do things at a software level and thus be able to be tweaked by cheats. This might also be something lost when converted to PAL (most systems that have a sensible resolution change option here are compiled code which means anything pointless and just going to take memory up might well get lost by the compiler rather than ignored for the sake of not having to do more work like 16 bit and older might have been) or changed radically such that you need a new cheat.
Some things might define a resolution you want to change, some might have it as a mode you can select/force by a cheat (if 0, if 1, if 2... works just the same as text speed up, flag based cheats like no monsters courtesy of potion, this button combo on title screen forces different language sorts of cheats, here you presumably playing on whatever selection menu the game provides and then possibly trying numbers outside what it gives you by normal menu options).
3) Cropping aka letterboxing. I don't know whether to hunt these people down first or those that stretch images not meant to be stretched (that is an option if the original devs make the textures designed to be stretched and look correct once they are, you lose some detail but hey). Not normally something I would expect to be seen done by cheats though, however it could be an internal option.
4) Emulator style camera rendering, though can be seen in hardware (the DS widescreen hacks for 3ds custom firmware users for instance, similar things also existing for GC games on the Wii). Here most things have an entire 3d world in memory and thus you can tweak the camera a bit to render a bit more of it. Some of these need cheats to also change some things (enemies might only move at the "side" of the screen which is now however many degrees in), if https://www.widescreengamingforum.com/wiki/index.php/Main_Page is anything to go by then you might need field of view, you might need to change the UI (some effects, UI elements and more are 2d images overlaid onto things which means your nice blurry/shadow lens effect is lost at the edges). There is also the emulator style take a savestate every frame, force the camera/player character (possibly disabling random battles and adding a noclip mode) to move either every direction (higher res) or left-right (widescreen, unless it is a vertical shmup in which case up-down might be the case unless you consider that it is probably just actually a TV on its side and...) and stitch it all together, other than those specific things that might do a wall walk and battle disable cheat then that is not really relevant in this.
**most conventional cheat engines, cartridges and the like often struggle to alter anything other than the basic RAM a console has with anything more specialist (which video aspects tend to fall under) in the hardware itself being off limits, that is until you realise the code (likely sitting in RAM for anything you are doing a widescreen cheat for and CD read speeds and latencies are brutal when your CPU is measured in hundreds of megahertz, if not gigahertz) can do it happily and thus change that to in turn change the normally inaccessible area. This then is closer to the more classical convert a gameshark/action replay/codebreaker/goldfinger/... code (AKA RAM code) to game genie (AKA ROM code, or for some reason assembly cheat in Switch hacking circles).
***video covering a few things here for N64 expansion pack, many of which I could see be activated by a very simple cheat (even those things not already gated behind a cheat in the "go here and enter this password/do a bit of finger wizardry on the menu).
