Yes, but. Certain types of glaucoma can cause eye ache (angle closure, inflammatory, neovascular, etc), but eye pain isn't a hallmark of glaucoma (for that matter, elevated intraocular pressure isn't either - about 1/3 of people with glaucoma in the US are thought to have "normal tension" glaucoma - ie the pressure falls in a "normal" range).
Not usually. There are many causes of headache and eye pain. In most people these are not related to glaucoma. Eye pain and headache occur when the eye pressure is very high (usu > 40 mm hg) or rises very quickly. This is typical of acute angle closure and neovascular glaucoma which also usu cause blurry vision. There are many flavors of glaucoma! Get your eye pressure checked and have a complete eye exam!
Yes. Acute angle closure or any acute pressure rise can cause and should be treated emergently. Can also have hazy vision and nausea. Much more common, chronic open angle glaucoma will usually have no symptoms even with very high pressures. That is why it is important to get checked regularly, especially if in a high risk group.
Glaucoma. Yes. Glaucoma is increased eye pressure & may be accompanied by eye pain as well as headache. See an eye doctor soon to have eye pressure checked, for untreated glaucoma can cause loss of vision. If you have glaucoma, the doc can tell you the options for treatment.