You’re definitely not overthinking things or overreacting to anything. Jeff is rude, lacks empathy, has no manners & no tact or paitence either.

He is definitely two faced & I don’t think that he likes teaching kids karate.

Hus rude comment about your partner was inappropriate. You shouldn’t let him talk to you like that. Document everything & complain about everything to management or H.R.

Touching Mary was inappropriate too. It sounds lije no one ever calls Jeff out on his bad behavior, so that’s why he keeps acting up.

You need to set firm boundaries with him. Honestly, drop that class & go to a better place to where the sensei has respect for other people.