Well, since nobody spoonfed me the answers to my questions, I got off my ass and found them myself.
First pic is the mechanical fuel pump. The black thing beside the hose clamp is the "fuel shutoff solenoid" and when I unplug it the engine dies. So it needs 12 volts to keep running.
Next pic is the boom/tilt function valve bank. One of those solenoids is the one that unlocks those functions. Still need to prove which one it is.
Third pic, unknown solenoid pointing straight up from the chaincase. Guessing it's got something to do with brakes or park brakes. Still gotta get into that.
I'm going to order a spare solenoid for both the fuel and functions, as well as a spare solenoid fuel pump. I don't think it's original to the machine, but helps once the mechanical fuel pump gets tired.