First of all, in an ideal world any person, male or female, adult or child, should be able to go anywhere they wish wearing, or not wearing, anything they wish. Unfortunately, we do not live in an ideal world.

For my part, that woman would be completely safe in my presence. Lacking actual, verbal confirmation that she does want it, and more importantly that she actually wants it from ME, she would be perfectly safe. NO means NO, always. And a lack of informed consent ALWAYS means NO.

Is it really all about power?
Are men really raping women because they hate women?
I think these go together. I don't see how someone could rape someone they actually hate. They may hate the fact that women APPEAR to have more power than them, and raping the woman destroys that power and demonstrates his own.

Why do men rape men in prison?
Is it true that sex plays a secondary or no role in this?
In large part this is still a demonstration of power. Yes, there is a sexual component, but I think the ultimate purpose is to denigrate the victim, basically saying to him, "You're just a woman here, and I'm the man."

They say most rape is done by people known to the victim. How does that fit in?
This has been shown to be so statistically, but you have to understand that a fairly large percentage of rapes are never reported. There could be many rapes by unknown persons that slip under the statistics because we don't know they have happened. You also have thousands of cases of women, mostly girls, disappearing every year. The odds are that the vast majority of these involve rape, but are not counted as rape in the statistics.

It is said that the social barrier to rape is much lower than the social barrier to murder. Is this true? And if so, why??
This has been shown to be true, many times. Look at the Steubenville rape case, for one. Students who admitted to rape were held to be blameless by their society because the were, first of all, boys and, secondly, football players. There also seems to be an element of classism and racism in rape cases. A rich white man accused of raping a poor black woman, for example, would be far more likely to get a pass from his society than a poor black man accused of raping a rich white woman. And especially in a a still largely misogynistic society, the female victim is more likely to be blamed for the actions perpetrated upon her. Happily, though, this seems to be changing. Slowly, too damned slowly, but it is changing.