Will Trump try to block oil exports from the United States?

I don’t know if he has the legal authority to do this, but does it even matter with Trump? 

Domestic prices will rise if 1) foreign supplies fall and 2) domestic production is diverted to fill demand overseas.  Trump could keep domestic supplies from being diverted and we could still use world markets to fill holes in domestic production. 

Of course, this would be an unspeakably crappy thing to do to the world, given that the whole supply disruption is our fault, but after some careful calculation we can determine that Trump gives exactly zero shits about that.

So:  Is this happening?  If not, why?

Beyond the military, every politician, dare I say every public figure, in America should make it clear that Trump is not acting in their name.

Spot on.