"I think you mean capacitor? Tone controls are generally a pot (the turny thing, it's a variable resistor) with a capacitor connected to ground.
However a piezo itself is a capacitor, so maybe they react differently, a picture or two would…"
"I'd say no on the pickup issue. If the strings are metal covered and the pickup is magnetic you are fine, I built a bass out an old strat copy, and kept the original pickups, does D0 (octave below standard bass E) just fine."
"It's a matter of taste, and playability.
Generally the strings are a little closer at the nut, and a little wider at the bridge, but they don't have to be. I'd suggest looking at some company that makes after market parts and getting…"