Yes. Any change from normal should be evaluated. Causes of drooping eyelid can include underdeveloped lid muscles, trauma, nerve or muscle damage, or even tumors or stroke-type conditions, to name a few. Knowing the cause of the droop (or at least ruling out the more serious causes) will go a long way to comforting you and providing treatment options.
Droopy eyelid. There are several causes of a droopy eyelid. Your best bet would be to have your eyes evaluated by a board certified facial plastic surgeon.
Depends. If your eye droop is of recent onset, it may reflect some neurologic issue such as a vascular change or tumor. Especially so if accompanied by a change in eye position. If gradual it might be a muscular problem or myaesthenia. Your ophthalmologist can sort this out and provide what relief is available.