No :teach: the PS4 does not work without a HDD. Because the filesystem is stored on there. So change the HDD and then update via USB. The blu-ray drive is not necessary.
Apps are fun. However, what more does it have to offer then what the browser can offer me currently? I never understood those 200/300mb apps that are basically a simplified browser.
This has to do with grounding of the whole installation. I face the same problems because I have no ground on my power lines (old house). I use special electric sockets that have a special filter in there to prevent this from happening...