Could an 18 year old be in charge of a nuclear reactor?

No, because they don't have the experience needed.  If he was smart and had a degree at 18, I wouldn't have a problem with the person working there, but not in a lead position.

Nowadays, sure.  Most modern nuclear reactors' computers will not allow the control rods to be pulled out too far.  There are many failsafe countermeasures to ensure that it is entirely safe, even if someone were to accidentally push the "wrong button".

I doubt it.

I hope not.

To be in a supervisory position you need an advanced degree and experience. At 18 the experience would be lacking.

Per Nuclear safety rules anyone 18 or below is not allowed in Nuclear plant where radioative level would be detrimental.
At that age radioctivity affect changes in their cells to a higher degree than adults.

Not as a supervisor.  And they would need A LOT of training.  They would have to be above and beyond smart and responsible for the COMPANY to even consider getting in that grey area.  If the public ever found out that someone not even old enough to legally drink was managing something that could kill them (ever hear story of 3-mile island?), there would be a massive public outcry.  And people would try to sue the company.  Being a 23 year old engineer and having a few college friends that work at the Perry Nuclear Facility near Cleveland, I've heard about all the training they had to do just to get in the door, and all the NRC rules they have to follow to do some basic stuff.  I seriously doubt it.  But good luck to you if can get the job.

Forget it.  You would not even be considered without a Master's Degree and 10-15 years of experience.

And there is much more to it than "supervising pressure."  Read a book or two about nuclear operations.

Not a chance.