I would say it depends on whether or not you know the person and how well you know her. I personally wouldn't mind if any of my friends call out for saying "What's up man!" or "Hey my man!" because I would consider those phrases to be sort of idioms that are not meant to be taken literally. If you want to sure whether or not it appropriate, the best thing would be asking the person herself, what she thinks about the issue. For a stranger or a random acquaintance though, I would not recommend using it because some people can take it as an offense.

No; people will think you are blind.

No, "man" is not used for girls. You could say "Hi, guys, what are you doing". "You guys" is often heard in California, for either gender, but not "my man".

It is the same for saying girl while talking with a boy. People generally want their gender properly labeled unless you are obviously joking around. If you make a mistake while not thinking, it is not a big deal. If you do it again, they will start correcting you because it becomes an insult quickly.