What is the difference between shall we meet and are we meeting?
is it correct "are we going to meet" too?

Question

Answer

"Shall we meet at 4pm?"  I am proposing that we meet at 4pm.

"Are we meeting at 4pm?" I think we previously arranged to meet at 4pm but can you confirm this?

Edit: "Shall we/Shall I" is common in the UK for proposals but not in the USA.

Answer

"Shall we meet?" is a proposal.
"Are we meeting?" is a request for confirmation.

Answer

All are correct, but there are some subtle differences:

Shall we meet - sounds slightly formal

Are we meeting? - this would be used more for inquiring as to whether or not a group is going to meet, not as a request to meet.

Are we going to meet? - this sounds like asking if something is going to occur, not a request

If you want to ask to meet someone I would phrase it as "do you want to meet?" Or "should we meet?"