They wont open the containers. Theyll just root around in your bag. Sometimes, I dont even have one of the "your bag has been check by TSA" tags after the flight
Yep, there's no issue flying with Homebrew, or most any other alcohol for that matter. Just make sure when you pack that it won't break open.
Most times when I fly, the majority of the baggage weight for my checked bag is booze, guns, and ammo.