1) "to geek-out" is an idiom (숙어) which means "to act like a geek". A "geek" is someone who is really into something, many times it is games and video games and computers, but now it can also be used if you are really into music or movies or whatever: music geek, movie geek, etc.
2) "to own what do" is also an idiom. It means "to be really good at what you do". Simple as that.