I live/work here. Fairly new Jeep owner but I've been out several times.
1. Honestly you'll have a hard time getting stuck. However, with all the rain recently there will be some nice mudding spots. As far as crossings, most are barricaded. You're not allowed to cross water.
2. If he's skilled he'll probably handle most of it depending on where you go. You might need to pull him out of the sand if he slows down too much but I 2WD a lot of the roads.
4. Download/bring the range map. You can get one at the Jackson Guard station. You'll have to go there to get a range pass anyways. The map is also on Avenza if you have the app for smart phones. Personally I've explored and enjoyed the area W of Hwy 87. There's a nice swim hole at the end of 767 in F1. Also some jeep playgrounds in Weaver Creek and G5.
5. Your standard gear should be fine. I'd have a tow strap just in case but the gas is unnecessary.
Also, before you go out have a plan. Check the Jackson Guard Daily Access Website here:
Jackson Guard Daily Access Map
It'll show you what areas are closed for the day. Usually that's due to testing or upcoming missions.
Shoot me a msg if you need more info.