I don't see why not.
13.1 is the latest firmware but if you're ever unsure, you can just check
Nintendo's website for what is the latest firmware. As for safe, some homebrew applications may not work on that high of a firmware so I'd only recommend updating if you absolutely need to. Homebrew and CFW don't work better on higher firmware versions. And as for where to find the files, those are copyrighted so no links nor help can be shared here because it would be the same as sharing a link to a pirated game.
If you mean use a homebrew save manager to dump the save files onto the SD card, then yes. However you won't be able to import any save data from your release day console to your OLED Switch without hacking it.
The biggest risks are breaking the pins on the Joy-Con rail but there has only ever been one reported case of that ever happening. I personally used a paperclip to enter RCM multiple times and have never encountered such an issue. For something like that to happen, you would have to exert a substantial amount of force, way more than what is necessary for bridging pins 9 & 10. I don't know which ones are safer but there a list of other items that people use to trigger RCM in this
thread. You are also correct in that you need to only boot RCM once and then you can switch to using AutoRCM so you don't have to deal with using a paperclip or something else to manually go into RCM.
Wait, hold on. What is this in response to? I never said to rename payload.bin to reboot_to_payload.bin. Reboot_to_payload.bin is only used when using the Restart function or your console crashes while in CFW.