These questions have been answered over and over again here. I'd suggest that you spend time reading the other threads rather than expecting regular posters to repeat the same thing again.
That being said, here are the short answers:
1. Yes, there are men in most, but not all, Barnard classes. It varies according to the class.
2. The way to take classes at Columbia is to sign up for them. There is no distinction between signing up for a Columbia class vs. Barnard class at time of enrollment -- the course listings are all mixed together. There is also overlap - some classes are offered at both campuses, depending on which section you choose or whether you take the course in the spring or the fall. Same course, but taught by both Barnard & Columbia profs at different times.