1) Definitely
2) Only if all else failed. A lefty that has enough arm to be a good catcher is more valuable on the mound.
3) No gain from LH to RH when throwing to 3B. Majority of hitters are still RH and he would have to maneuver around those guys regardless of throwing hand.
Have your son use that catcher mentality to make the team better from another position. Best of luck.