Can a 16 year old get insurance on his or her car without having to have a parent on the insurance too and without having to be on their parents car?

No. At 16, you're still considered a juvenile in the eyes of the law. As such, you can't enter into a legally binding contract, which is what an insurance policy would be in effect.

Not to mention that a 16 year old would pay an outrageous amount of money for insurance, as that bracket is the highest risk.

You can, although most insurance companies will not. if they do you will be paying stupid amounts of money for 3rd party only . On my 16th birthday i got insured on my 1.3L VW polo on my own, my parents didnt even know. Though it did cost me £1459, for 3rd party only, rightly so as a crashed 3 days after passing my test haha. didnt beat my brothers record of 2 hours though. I personly don't think 16 year old males should be allowed on public roads =p