A headache is a symptom not a disease. Nearly all headaches have a trivial or nervous cause. However, a headache can be a symptom of a more serious condition and that could be fatal.
Depends on what it is caused by. Most of them, no. However I experienced a headache caused by a burst, malformed vein in my brain that could have very easily taken my life. I had to undergo surgery to have this repaired which disabled me. It was by no means a simple headache. It was as if someone was bringing a sledge down on my head.
Yes if it turns out to be a brain haemorrhage or a stoke but usually there would be several days of headaches.
There are also Cluster headaches which are so severe they are also known as suicide headaches as they can be so long and so many that the sufferer takes their own life rather than have another bout of intense pain.