Hi,
I expect you are right about the floppies degrading, lots of mine have died. Suggest you have a look at getting a Gotek or HXC drive for using USB instead of floppies.
Might have persevere with the mouse, not sure why it would be so stiff. You can buy Amiga to PC ps2 adapters to use more modern mouse.
Amiga to RGB / Scart would probably the best picture you can get from a stock A500.
Not sure about the guru/ram expansion problem, maybe someone else on here can suggest something.
Hard disks are a bit of a pain on the A500, a few expansions around. I quite like the look of ACA500 and the Vampire 500. Although slow the Gotek is a good starting point
Probably a good idea to open up the Amiga and just check things over, personally never needed to replace caps in any of my Amigas or other old kit, maybe my stuff has had an easy life. Read a few other posts about caps in the PSU so have a look at that as well.
Good luck
Oli