Aztruck,
The simplest thing for you to do is do your renewal online. There are plenty of refresher courses available. I know jepessen and asa, king have them. I know they are not expensive but don't know what they entail.
As for flying your aircraft if you are not doing any training in it towards a rating you CAN fly it on your tourist visa. This is to the best of my knowledge, dealing with a lot of international students at the flight school I work at in the US.