1) Yep.
2) Kinda. Yes if the engine isn't running, and yes if the alternator has failed!
3) It depends on the battery - different batteries supply different voltages, depends on your aircraft systems. You might also have regulators to give different voltage feeds, and/or have an inverter on a more complex a/c that provides ac power from DC, but unlikely on warrior types.
4) It recharges the battery, and provides power for the systems when the engine is running. Think of the battery as a resevoir.
5) depends on the ammeter and how it is wired. Some are centre zero and show flow in/out of the battery - they will read positive when the battery is charging, and negative when it is draining. Some are showing load on the system and always deflect in a positive sense - it's worth knowing what your usual load is.
6) if it's a 24volt alternator, sure. Depends what it was designed for. That's rather aircraft specific.
Also note that on most aircraft there is some sort of arrangement with the master switch that allows you to switch the alternator / battery on separately.