1. Ours get the mineral/salt licks 24/7 365 days a year. They drink more water, and don't browse in the dirt for the minerals.
2. Yes- all our horses chew on wood, whether it's the fence or the barn stall. Even when there's stuff to do, and hay to eat. And one is a stallion, so it's not really exclusive to the sexes, that I've observed. If his chewing really bothers you, wrap the wood in sheet metal, and he won't ever try to chew it again. We did this- pried up the top boards on the stall gates and wrapped them with the sharp edges underneath- and they've stopped since then. You might also try stuff that tastes really bad, but that's harmless, like Tabasco sauce.
3. Yes, one of my geldings has "stallion" tendencies. We had a pony mare, and he went around "helping" her out all the time. It really depends on your gelding, but they should be fine. The little mare nailed him a few times, and that was the end of it.
If you have one that's recently gelded, be sure to wait at least 6 weeks before putting him in with mares. A friend's mare was in the pasture with a newly gelded stallion and -Oops!- she got pregnant. LOL, just something to be aware of.
4. WOW!!! That's AWESOME!! Big congratulations! He must trust you a lot!