I am thinking of bringing my car by sea.
Had I known this was possible we wouldn't have bought the panga. 
Should I keep my license plates or get new ones in Mexico?
You must keep your US plates. It is VERY difficult to re-plate a car here....requiring the greasing of many pockets.
How do the Mexico authorities verify if foreign plates are still valid?
They can't and don't care. It's a beautiful thing. My buddy John has Texas plates that expired in 1991.
I would insure locally in Mexico, is that possible on foreign plates?
No problem at all.