I always fist bump, no hand shaking unless it's someone that I know, then it's a handshake or "bro hug". The most important rule, IMO, is to always be respectful. That alone will avert a lot of hassle. Always acknowledge people, I never just ignore (it's just rude). Be decent, and you won't have many issues.

As to the locals crossing the line with your lady, it has never happened to us, as long as I'm present. The locals have always been respectful in that regard, at least in my experience. But I'm always with her, so that helps a lot.