I'm just starting out skateboarding. If I push with my left foot am I goofy or regular? Also would I be considered mongo if my right foot is in the back on my board? Thanks!

You ride regular since your left foot as at the front. The foot you push with does not determine stance. Pushing with your front foot is pushing mongo and is generally considered unacceptable by most skaters

If you are left handed and pushing left footed, not goofy at all. my opinion anyway. Now it gets complicated if you are goofy and want to pop the tail with your right foot and don't like riding mongo.

If you push with your left foot Your goofy. Also It's better to not push mongo because it's harder to get your foot set up for tricks.

Don't change your riding style i have one 4 skate board tournaments and I ride goofy and I have never changed it and I never will.