What happens when a gate moves onto a vortex?
Moving gates cannot move onto Vortexes.
From a post on Fantasy Flight's forum:

Gates can't enter Vortexes. In this situation, the vortex is treated like an open gate, and gates can't move onto gates.
If a gate has to move into a vortex, it just stays in place instead.

I do not believe that the answerer, Tibs, is an official representative of Fantasy Flight.  However, he has nearly 4000 posts in their Arkham Horror forums and seems to have a very good grasp upon the rules.