If I live in my parents' house but I am 18 years old and I pay for my own car insurance, can you legally take my car keys away?

You may be paying the insurance as a condition to be able to drive it. Is the car titled in your name, or yours? If it's in his name, it's his car. They can take the keys. If you are titled in your name, they can not legally take your car away, but they can throw you out at 18. They are giving you a choice, and perhaps a not so subtle clue that maybe it's time for you. To leave the nest, fence for yourself. If you want the safety of your nest for a longer time, then fly according to its rules.