Q#1: There are punishments, if it can be proven. Slander- you can't make false statements about someone without the facts to back it up, if damage is done to the persons reputation, business, employment it can also be taken to Civil Court (USA). Perjury as another answerer stated, if the case has been in court and it can be proven that the victim lied about the rape,harassment, etc.,.
Q#2: Many times rape, harassment and molestation cases go unpunished as they are hard to prove. Therefore the victim suffers without seeing justice prevail.
Q#3: covered in ^^^
Q#4: If the woman is the obvious weaker person in the domestic dispute, yes, usually they side with her. If they show up and the woman is built like a line-backer, they would be a little more likely to hear more of the story and determine that she was perhaps the abusive one. Think this one is based on perception of what is seen by the officers when they arrive at the scene of a domestic dispute. Where I am from, they have to take one of the parties to jail on a domestic call, most of the time, yes it is the male.
Q#5: Yes, it's been done many times. It's not as common, for several reasons, not as many women have that kind of power over a man in the work place, men aren't as offended by sexual jokes, flirtations, etc,.
It sounds as though you are close to a case gone bad for lack of evidence either way. It goes to show that you can never be too careful who you're dealing with, and to always be leary and cover yourself in any / all situations.