it could still be a tumor, or even an abscess (abscesses are at least easy to drain at home).. rats don't usually...get... bumps.. from falling
Also, yes they'll sometimes lose fur when they get a tumor depending on the location.. most of my experience is they'll lose fur if they get ovarian cysts
Also, a brain tumor usually results in seizures, until they die... I've had one rat with it before and let me tell you that seizures are in no way fun to watch. you wouldn't be able to see a brain tumor....