I see this piece is dripping oil somewhere. Can someone tell me what this is, and also, do you think it’s just a gasket? Or does something more major need to be replaced. Thank you!

 

If it's oil could be the rear seal on the engine, if it's transmission fluid probably front seal on the transmission. Either way the engine and transmission have to be separated to repair.

 

Looks like the rear main seal has failed. If it was the transmission front seal it would’ve dripping from the bottom of the bell housing as the torque converter comes first. For oil to be on the outside of the inspection cover it almost has to be the rear engine main seal.
The fix is to pull the engine OR the transmission so as to be able to pull the old seal out and put the new one in. The seal is probably $20 or so but the labor is horrendous….sorry.
It doesn’t look that bad…I’d just buy a case of oil

 

Was it running ok when you took it apart??