TMJ. Tmj can cause headaches however it would probably be best to first see your medical doctor. There are so many headache related medical problems.
Sometimes really bad. Tmj can cause severe headaches, usually on the side of the head or the side of the face or jaw. However, headaches can also be caused by more serious things, so you should probably have them checked out by a doctor. The good news is that, if your headaches are caused by TMJ problems, then treating the TMJ problem will often relieve the headaches.
Severe. Sometimes TMJ headaches are severe, sometimes worse than the associated TMJ pain.
Varies. Headaches are often a combination of triggers, tmj/tmd just being one of them. The intensity and severity often depends on the person and their pain threshold. I would see a dr. And then determine if a tmj/tmd specialist is the next step.