Regret is not ever rape. I question from what sources you are getting your information if you believe so. What can happen is that someone who was too intoxicated/incapacitated to give consent to sexual activity can make a complaint because sexual activity occurred without voluntary, freely given consent.
If you have power, many things can be considered harassment, which is different than assault. It's similar to the reasoning behind prohibiting psychological therapists from engaging in sexual acts with their patients.
Really, it's pretty simple. Make sure a person can give consent. Don't abuse your status to obtain sex. Don't rape.
Not in the USA, it can't. Some darker corners of the internet say that's the case in Sweden, but even then they're mis-stating the case.
In the USA, even rape is often questioned as rape. We've had national politicians make false claims about "legitimate rape," and how rare that was.
In no case whatsoever is there any idea that "regret = rape," and if you've been led to believe that about the USA, you've been in some very disturbing places on the internet.
Are you getting it confused with sexual harassment? which we are also talking about in this thread.