My tooth is hurting after getting fillings. Does it sound abnormal?

It's very common. When a dentist places a filling heat is generated - that's what makes your tooth hurt when getting a filling and why the dentist numbs you up. If the nerve is traumatized by the process it may hurt after the numbness wears off.
Depends. If the fillings were deep pain is more likely to be present, but if the fillings were shallow i would say that it is unusual. If the pain does not start to subside within a few days i suggest you call your dentist.
Not uncommon. Many times fillings can be deep and near the pulp/nerve and though they don't get there it can be irritating like a bruise. It should peak over the first couple days and then taper off, if not contact you dentist.
Possibly. While some sensitivity after filling is possible due to irritation of the nerve, especially if there is a deep filling, prolonged sensitivity may indicate irreversible nerve inflammation.