In answer to your first question, a headache that is persistent is not necessarily a brain tumor. A chronic headache can come from lots of things, the most common are some kind of sinus or tooth infection, bad muscle strain in the neck or shoulders, vision insufficiencies that need corrective lenses, and migraines.
Usually a brain tumor is indeed accompanied by other symptoms, for example speech or memory might be abnormal, depending on where the tumor might be located. Diff parts of the brain, if pushed on or dying, will produce diff symptoms in all diff parts of the body. So, if a physician notices you don't pass a simple neurological office exam, like touching your nose with your eyes closed and answering questions, then the best way to determine if a person has a brain tumor is to do a scan of it, and then look at the pictures to visualize any abnormality in there. Hope this steers you in the right direction.
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