Brainwashing, or mind control, is a fairly new term, actually. It came about in the mid-1950s when the Cold War was at its peak usually involving adult Prisoners-of-War (POW).
First, if your character knows no other way, it isn’t brainwashing. Brainwashing involves elements of forceful re-education, which often includes torture. With that being said, small children are information sponges. They’d typically get sent off to school, where the curriculum includes a heavy dose of propaganda, along with reading, writing, basic math. Depending on who is churning out the propaganda, you may either see sciences being restricted (in the case of a religious cult) or them being emphasized (typically with totalitarian regimes). Why are sciences emphasized? They need engineers and scientists for their military projects.
With that said, finding out everything you know about the world is a lie isn’t something you bounce back from in a couple days. Some people sink into depressions for months. Some people become drug or alcohol dependent to cope. For those who decide to leave, it’s a long dangerous road. Some are sold into sex slavery by human traffickers. Some are caught and executed. The few who do make it are left trying to navigate a completely foreign country. If it sounds bleak, it is. If you want to know more, I’d look into North Korea.
As for your second question. one of my favorite resources for all things fighting related is the How to Fight Write tumblr. They have an excellent tag on assassin related resources and answers to questions. The tvtropes.org website has a great list of related tropes you should be aware of if you’re going to write an assassin, too.