"A young Jedi named Darth Vader, who was a pupil of mine before he turned to evil, helped the Empire hunt down and destroy the Jedi Knights."

That's how the quote goes, I think.

How could he be a Jedi while hunting down and killing other Jedi? I would think that his actions against the order would make him something else entirely.

I think it means he was young when he first became a Jedi (not necessarily making Obi-Wan substantially older).

There's nothing to indicate how old Vader was when he fell, how long he had been a Jedi, or how long his quest lasted. Anakin could have been in hiding for years and years before conceiving Luke. It's not like it all happened on the day Luke was born (pretty much the impression we get from the retcons we have now).