Welcome! That's a sharp looking 107.
For the pulleys, you can check the sponsors above, or poke around on e-bay, or post in the wanted section. They are fairly easy to come by. Check out parts tree for the part #s, and go from there. The mule drives are pretty much all the same as it relates to mowers.
I believe the belt p/n you want is IH-489397-R3. Belts are sort of like religion around here, but make sure you get a decent one, as the mule drive takes a toll on them. Some people like NAPA ones. Some people swear by Stens. Some say only the CC/IH ones are worth a toot. You'll rarely go wrong with OEM, but I have a stens one that works just fine too.
There's a
link in the technical library to the reference manual for belts that will give you the details.
That looks like a later 48" that's in pretty good shape still, but it's been repainted and it's kinda hard to tell what sort of shape it's really in. The decks don't have serial numbers on them, per se, just a model/revision number. I don't think there is much difference between the U1113 and U1116, but I'm hardly an expert. Probably just in the alignment of the anti-scalping skids and whatnot. The 107 would have had a 38", 42" or 48" deck on it. The 48" might have been a bit much for the 107 to push through tough stuff, but it's a pretty good deck.
That QA-42 thrower looks to be in pretty good shape too.
It looks like everything you have there has been repainted.
As for the charging system, it's very common for the voltage regulators on these things to stop working. It's also quite common for there to be broken wires, as that tractor is pushing 50 years old at this point, and the original wire loom is getting brittle and corroded. Do some searching, and you'll figure out pretty quick what is wrong. A multimeter is very helpful. I don't think those headlights aren't original to the tractor, though they are tastefully done, so who knows what's happened to your harness.