Question

1. Are you driving after work.
2. Will you drive after work.
(Does #1 mean #2?)

3. Are you driving tonight?
4. Will you drive tonight?
5. Shall you drive tonight?
(Does #3 mean #4 or #5?)

Answer 1

"will" and "shall" are synonyms. They mean the same thing. They mean the same thing as #3.

1 & 2: "Will you drive..." might mean "Are you willing to drive..." OR "Are you intending to drive..."
"Are you driving..." is more definite, meaning, "Are you going to do it...?"