You will need to run some fan speed/ temperature monitoring software since the SSD will not have the Apple firmware in it to report back the drive temperature to the sensors on the logic board. This is the one I recommend: http://www.hddfancontrol.com/ It's not free but is actively updated and supported for new versions of the OS. If you don't run software to do this, the machine will run okay for approx 30-40 minutes at which time the fans will kick up to high speed and be very loud. This won't hurt anything but will be very annoying and you do run the risk of burning out the fans quicker since they will be running at full speed. Other than that there shouldn't be any problems running the SSD. Just be very careful when removing the display panel. Because the glass and the LCD panel are glued together you have to be very careful when cutting the adhesive strips that attach it to the rear housing so that you don't crack the glass. As far as I know there is not replacing the glass panel only if you crack it...
There are two most likely problems that could be causing your issue. First, if the iMac has the original hard drive it may have failed. Hard drives can sometime fail in a way that will prevent the boot sequence from proceeding when using other boot sources like your OS system discs. If it does boot from the discs then try to open the Disk Utility program and check to see if your hard drive appears on the left. If not the drive has failed. Second, the G5 iMac's are notorious for having issues with the capacitors failing on the logicboard (like may other computers of the time). I would suspect that if you open the machine up and look at the logic board you will find the capacitors bulging or popped. If this is the case you have a few options: have the board replaced with a refurbished part or have the board repaired by someone who can remove and re-solder new caps in their place. Good luck
You most likely have a stuck keycap or got some liquid in there. You can see what keys are stuck on by opening the keyboard viewer and attaching the keyboard. I'm sorry to say either way these keyboards are not repairable in my experience.
It is possible to replace the key as long as the tabs on the back of the keycap are not broken, the scissor assembly is intact and unbroken and the rubber bumper is still attached. If the scissor came off with the keycap you will need to disconnect it from the back and attach it to the keyboard first. should look like this: Then snap the keycap back on starting on the left side to seat it on the scissor and finishing by pressing the right side to snap it on. If it doesn't seat and stay attached there is most likely a broken tab on the keycap or scissor.