#1
I've tested the bass on a couple wires and amps, so i know its not the other gear, whenever i take my hands off the cable in the jack, it makes this loud-ish hum. It is an Epiphone Thunderbird, and has worked fine for the two years I've had it, i have a feeling it has something to do with the ground, and i have a soldering gun and solder, i used it on model cars to work on little engine thins, so i know how to use it with mild ease.
#2
I think you're on the right lines personally and that's where I'd be inclined to start.
#3
Ok, I have this problem too with my bass. Whenever I am not touching something metal (tuning pegs, strings, knobs, jack), it makes a buzzing noise. I've been curious about this for like three years but never bothered to figure it out.
#4
That's normal but more noticable on a bass with single coil pickups, there's an earth wire goes to the bridge so when you're touching anything metal it earths through you.