What happens to Bella's parents after she is turned into a Vampire?
they remain human
She was, put into a mental institute for "seeing" though I'm sure it wasn't as powerful as it is after she's turned. Her parents pretended she had died as soon as she was admitted. Sometime after that, James went after her for some reason and an older vampire turned her so she couldn't be hunted anymore.
There are many different legends. In Twilight, you either die or get turned yourself by the poison. According to the Twilight book series, if you get bitten by a vampire, you get poisoned by their fangs. This poison can either kill you or turn you into a vampire. You can also be exsanguinated before you have the chance to change.