If you really only change the CPU, nothing will change. Except maybe better transcodung performance.
But you’ll have to research if you really can upgrade just the cpu. Usually/often replacing the cpu requires you to replace the motherboard as well.
Which in turn can also require you to replace more components, like RAM, PSU or graphics adapter.
If you can get Windows to run again, without having to reinstall it, then no.
If you have a hard drive/SSD to spare, you can move the plex data folder to it. This should enable you to get up and running quickly, even if you have to reinstall your machine.
Just make sure that all your media continue to be available under the same drive letters and folder names they are using now.
Opposite of what?
The moving procedure? Generally yes.
But if you like to keep the data folder on this separate drive (if you have a case with plenty of space), then you just need to point the newly installed Plex server to this extra drive.