Hi i currently have 14" wheels on my fabia and was wondering if 15 or even 16" alloys would fit in the wheel arch without rubbing or damaging anything?

Yes

Yes depending on width and offset that is. 17s will fit fine with the correct size tyres aswell.

No they won't. Oh wait, yes they will. But then again... I'm not sure.

You shouldn't have a problem with 16's

16s with 205/45/16 tyres for certain. Or 205/40/17 for 17s IIRC