How long to charge battery on shore/generator: Shore and generator are the same. It's being charged by the converter in both cases. How long it takes depends on how dead it is, and how big your batteries are. If you have 200 Ah that are totally dead, and a 55 amp converter, it would take about 4 hours.
How long to charge batteries from engine: No idea.
Yes, you can replace your generator with a diesel one, but you have to really want to. $$$$$ Take a look at a propane extend a stay as a less expensive option. (If your build sheet said you were getting a diesel generator, you need to get that fixed by your dealer. It's a very expensive option!)
Your propane furnace runs off 12V power for the blower and control electronics. It will run off the batteries just fine, but will drain them pretty quickly. The blower fan takes a fair amount of power. How long you can run it before you need to recharge the batteries (assuming you don't have solar) will depend on how much it actually needs to run, but generally speaking, a couple nights is all you can get.
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2021 Thor Four Winds 26B on Chevy 4500
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