According to Human Rights as known. Do humans have the right to brainwash? Do humans have the right to prostitute?
I don't know what universal definition of human rights you might be referring to. But I'm a libertarian and our philosophy is fairly simple. One of its cornerstones is: Consenting adults have the right to do anything they choose, so long as they cause no direct harm to others. This specifically includes doing anything we want with, to or into our own bodies. So drugs, risky sports, unhealthy food, tanning, odd sex practices, and the like are all permitted, so long as they are consensual and the people involved are adults.
Therefore prostitution must be permitted. It's your body, lady, you get to decide what you want to do with it. If you want to use it to make money, it's your choice.
Brainwashing, no. Unless you're talking about that cool TV show "Dollhouse," in which the subjects contract to have their memories rewritten every week, are compensated for it, and get their own memories back after five years.
Obviously in the real world there are no absolutes. I'm familiar with the concept of situational ethics: choosing the least bad alternative when no alternative is perfectly good. Just as occasionally there is no alternative to killing someone, perhaps once every few years there's no alternative to brainwashing someone. Maybe it's for the greater good, like forestalling an act of nuclear terrorism, and we can't figure out any other way to thwart the terrorists. But these instances had better be so rare that there isn't even a name for the practice, and the people who do them had better be haunted by them for the rest of their lives and work to build a world in which they won't be necessary any more.
If yes, why do almost all 'human rights' loving countries have problems with prostitution?
It's because in practice much prostitution is not a consensual decision. Many young girls are sold into prostitution by their families in poor countries. Others are captured in wars, kidnapped, or convinced by the lie that they're being smuggled into a new life in a more prosperous country. So prostitution has a pretty bad reputation in most of the world and it's easy to understand why decent good-hearted people are opposed to it.
Here in the USA many (but by no means all and probably not even most) prostitutes are drug addicts who resort to prostitution to support their habit. Of course as a libertarian my attitude toward that is that drugs wouldn't be so expensive if they weren't illegal, so it's all the fault of the goddamned shit-for-brains government. In any case the lady knew the risks when she started taking the drugs, so it's not easy to argue that her plight is not the result of her own consensual choice. And every now and then we get a boatload of those girls who were told they were coming to America to get jobs as maids and factory workers, and they end up as prostitutes. It's been said (and I cannot verify this assertion) that many of the men who manage prostitutes' careers ("pimps') deliberately get them addicted to drugs so they'll be easier to manipulate. I do know enough about the phenomenon to know that not all pimps are dishonorable and some of them really are fairly competent managers who make sure their girls are treated decently and get a good wage--because of course that's more money for them too.
Governments have a trick that they often use to sway public opinion against something they want to prohibit. They make it illegal. That automatically pushes it onto the black market where mobsters and other criminals will be involved in the business. Eventually it begins to look rather sordid and the general public will be outraged by it. That's what they did with recreational drugs, and they've also done the same thing with prostitution.
In one U.S. state, Nevada, prostitution is legal (except in the big population centers: Reno, Las Vegas and Carson City), and it's like Holland. The girls have clean establishments in which they work, they get medical checkups regularly, it's a regular job with a schedule, sick leave, vacations, insurance, etc, and it's run like any other business. There are no drugs, no one is ever harmed, they turn away clients who look like bad news, and the girls can leave whenever they want. They make decent money and some of them are just working their way through college.
If prostitution were like that everywhere, there wouldn't be so much antipathy toward it.
Of course the other reason is that the Abrahamic religions (Christianity, Islam, and to a lesser extent Judaism) consider sexual intercourse to be a sin if it's not between a husband and wife. So their campaign against prostitution is simply their attempt to force their religions on all the rest of us. Apparently they're not good enough for us to voluntarily accept them, the way we accept really good food or music without having to be forced.