When I first got my bike the starter was turning but the engine wasn’t. That turned out to be the main outer gear turning inside the starter when it should have been fixed solid. I packed mine out so it was clamped tighter when the two ends of the starter were bolted up tight. It’s still working..
Sounds like you have some serious issues there. It may be worth bearing in mind that the alternator on the twin needs a voltage fed in to get a voltage out (inner coil is an exciter coil which has a voltage varied by the regulator to maintain the voltage of the output at a set rate) if the battery voltage was low then the charge rate would be low, although my bike has charged from a battery which only just ran the neutral light 🙂
Michael is correct in saying the 3 outputs from the alternator (yellow wires) can go in any order as they are just feeding through a bridge rectifier to be turned into one direct current voltage into the regulator.
