You can use liquid makeup remover and a tiny baby bottle brush or a pipe cleaner, or you can just pour the remover into it and shake it until the makeup is diluted. Then just wash it and you're done.
Give him a little journal with a "how to survive" guide, and write tips and such. He could also use a wallet to put spare change in, and just whatever...
That would really just be a large spray bottle. If you were looking for a water gun with more capacity, I would recommend sizing up the whole project to larger...
No, your skin has to be drenching wet. It's a super common misconception, but your skin has to be totally soaked. You cannot apply makeup to dry skin, period.