1. The tach drive on the generator is probably stripped/worn out. Given that the charge light is on... it's probably not charging. Given this situation I'd probably opt for the alternator conversion for that tractor that includes a tach drive on a Delco 10si alternator. YT sells the kit.
2. If the tach needle moves the cluster is probably OK. The proof meter won't move until you get some sustained use on it as it's tied to the tach internally.
3. Wiring... you can buy a harness but for an many wires is on that thing (plus considering you're going to convert to an alternator) it's probably just easier to patch/repair what's there and reconfigure the rest as necessary. If you have a wiring diagram that's about 90% of the chore... so follow that and you should be able to make it work.
4. covered in #1.
5. That could be one of two things. Either the voltage stabilizer on the backside of the fuel gauge is bad and allowing full voltage to go to the instruments... or the wire to the temp sender is bare and finding a direct ground path. Third option is a bad/shorted sender. Of the three possibilities odds on one and two are about even. Bad sender is very rare...