Hey, good work, sounds like a good buy.
1- Yep, dex III for trans oil. I like to drain using the transmission drain plug, refill, drive it a couple days then drain again. Repeat until the fluid is red. Only problem is this doesn't clean the filter.
2- Dexron III for transfer case as well. Make sure you remove the fill plug before you remove the drain plug. Just in case you can't remove the fill plug...
3- No specific jeep coolant, just get something with a good anti corrosion package, nulon is a good brand..
4- Just standard diff oil 75W- 90 for front and rear diffs. It's the most common one. It usually has an anti slip additive included, will say on bottle. If you have the crappy d35 rear diff and wanna tow or anything its good to use thicker 75W-140 oil in the back. Synthetic helps too.
5- Use genuine jeep power steering fluid from the jeep dealer. Its clear. It's not too expensive, around 14 dollars per container i think (900 ml or so). i have read somewhere that there is a valvoline synthetic power steering fluid that you can also use.
Prob not a bad idea to replace the mounts, i don't know too much about that stuff. Check
http://www.greatlakesxj.com/tech.html for factory workshop manuals and
http://jeep-xj.info/ for handy info..