Battery post / cables

4/0? If spending money there is no reason not to have the right stuff.

http://www.genuinedealz.com/custom-cables?size=46

Otherwise yes the 3/8 should be fine.

No. What counts is the contact area around the bottom of the threaded post that the lug is to sit on. Some are wide and flat and others are sort of not so flat, reducing contact area.

If the latter, you can use a copper flat washer so the lug will be tight when bolted down. Not ideal, but what else can you do?

Ring lugs are also either lumpy or flat. flat is better than lumpy for contact area. Stacking lumpy ring lugs is a loser. Avoid stacking where possible by using a buss bar.