Ok then i am a spark so basically the extract fan sounds like it is 12v or 24v you should "check first" though. if it is either of those voltages you will need a transformer if there is not one already built in. If it is 230v you should just take a live and neutral from a light fitting and connect through in a joint box or a spur.
About the lights going off with the steam i would just check that all connections are tight firstly and if that dont do it, it could possibly be the switch but it sounds abit weird to me, is it just the bathroom lights that go off? where abouts are you by the way?
i have never come across a 24v fan for household use
nor a fan with the transformer built in, that would kind of defeat the object would it not ?
surely if anything this would be a smarter option considering the enviroment it will be in?? humid/ect low voltage and that .. but im sure it should be of a certain IP protection.... and ofcourse on a RCBO ;)