You can feed on anyone, and it doesn't hurt them so go to it. They look very human, if they feed at least once a day (every 24 hours). Vampires in Cyrodiil work a little different from the ones in other parts of the world.
If you neglect to, or choose not to, cure it, then you will become a vampire.
If you catch it by accident, just use a Cure Disease potion, spell, or get to a Nine Divine alter within three days and you'll be fine. Everytime one of them strikes you in melee, there's a chance that you'll catch "Polypheric Hemophilia." That's vampirism's early stage. Just find a vampire den, a cave or tomb inhabited by vamps, and fight them. The other way, catching it, is somewhat simpler. One is a reward for completing Dark Brotherhood quests.