Did you check the transmission fluid while the engine was both warm and running?

This type of caliper needs a special tool to get the piston to retract, these can’t just be pushed back in, they have to be twisted in. If the piston isn’t falling out of the caliper and there isn’t any fluid seeping around the piston then you might be okay, most auto parts stores have the tool you need to twist it back in for rent.

I agree, go to a shop that does mostly exhaust work. Dealerships and most common mechanic shops don’t have the equipment to repair exhaust systems like a muffler shop would, so they tend to try and sell you new parts vs. repairing broken things.

Sounds like you have air in the brake line somewhere. Try bleeding them again, remember to start with passenger rear, then drivers rear, then passenger front, and then drivers front. Double check all the lines where the connect to the calipers for leaks as well.