yes, because even though your a legal adult you live in their house and follow their rules. if you want to be in control of yourself and still live under their roof, offer to pay a rent of sorts, or you could move out and get a job (not necessarily in that order)
No they don't. You see, it's their house, so it's their rules. Yes you are obliged to follow their rules but no they can't control you. If you don't like or don't want to follow their rules you are perfectly free to move out and pay your own rent and bills in your own place. It's all about choices.
it is called respect. if you want it, you need to give it. if you're going out, let them know. if you're going to be late, let them know. just because you turn 18 doesn't mean you're grown and can fend for yourself. and just because you're an "adult " doesn't mean your parents should stop caring.