1. I have used both and never had a problem, I did use the Army painter primer in both cases, I know there is a lot of criticism of the Army Painter primer, but personally I have never had any issues.
2. Cutting it with a bit of turpentine would help, I would say anywhere between 1/4 to 1/3 thinner is about what you want to shoot for. I have found that Army Painter tends to be a little thinner than Minwax. When brushing the Army Painter on it seems to be more subtle, whereas the Minwax seems to be more dramatic.
3. Ideally you should paint all details before applying the wash, after it dries if you need to clean up edges or pick out details your should be fine.
4. I think you would be better off with the Strong Tone.
Lastly here is a nice guide to dipping that I always found helpful;
http://gfbrobot.com/2010/12/03/andrews-guide-to-dipping-minis/