1. I would like to confirm whether there is a class today of level 3 English with Miss Mary.
2. Can you confirm for me whether there is a class today of level 3 English with Miss Mary?
"Confirm" doesn't require a person as an object, so "confirm me (that...)" is not correct. Either rewrite is OK, but I'd choose the first sentence for the sake of clarity.
"Whether" implies "...or not." You could replace it with "that".