Hitting - Maybe true if we're referring to a slap, however I'd never call it brave. If women thump men very hard, so as to inflict injury, then obviously she'd be frowned upon, just like men. I think the reason men are generally berated if they hit back is because they are just far more likely to cause damage.
Kissing - it's pervy for both if it's someone you don't know! In what universe can I go around snogging random blokes for no reason and not be chastised?
Bathroom - yeah, maybe pervy if you hang around. Normally its the same for both, it's obviously a mistake if you just quickly turn back.
Staring - No. I don't think staring at a man's crotch is a common, effective. or acceptable flirting technique.
Splitting the bill - it's quite common to split the bill now. Really don't see the problem.
Police - Men have the same right to file sexual harrassment claims as women (taking the example of work) and claims against women has risen to around 15% of the total - in the US at least, couldn't get reliable data for UK but I assume it's similar. Your problem is getting better.