SATA III is backwards compatible with SATA II, which is compatible with SATA I, although I'm pretty sure the 2012 model uses SATA III so your SSD should install with no problems. I think to use your old HDD as an external HDD, you've got to use a caddy and a USB to SATA cable.
The trackpad is normally above the battery and if it is becoming squishy and unresponsive your battery may be swelling. Check your battery status. If it isn't a battery swelling issue then I'm not sure.
Sounds like a logic board fault. Not much you can do besides replacing the whole logic board. You might have some luck with ghetto methods such as leaving it on and overheating it on purpose by turning it on and leaving it under some blankets (if it turns on, but refuses to boot i.e fans still run, MagSafe turns on). Otherwise, you might be outta luck. EDIT: Realised you said nothing turns on, seems like a power issue with the logic board.