Do the UFOs over the continents get removed when they raise the terror level?
The UFOs will remain over the continent, provided the continent's panic level has not reached orange (panic).  Once the panic level reaches orange, all UFOs over that continent are moved to orbit.  

According to the electronic rules (Download the app -> Menu -> Rules -> UFOS) or the Rules Reference p11:


  If a continent has fallen into panic when updating the panic levels in the app, all UFOs in that continent are added to orbit.


Also as it has in the electronic FAQ (app -> Menu -> FAQ):


  Q: Do UFOs remain on the board after increasing panic?
  A: Yes, UFOs remain on the board until destroyed.