When using Alvin & Dexter with TtR:Europe what are the rules about cities with existing train stations?
These questions, along with a few others have been officially clarified by Alan R. Moon on BGG. His rulings regarding your specific questions are bolded below:


  Here is a list of the official clarifications I'm keeping for Alvin &amp; Dexter:
  
  
  A Station cannot be built in a city with a Monster.
  A Depot cannot be built in a city with a Monster.
  A Passenger cannot be moved out of, into, or through a city with a Monster.
  A Monster can be moved into a city with a Station, Depot, or Passenger.
  If a Monster is in a Country location, the whole Country, not just the specific space, is in Chaos.
  Cards cannot be added to or taken from a Depot in a city in Chaos.
  At the end of the game, a Station in a city in Chaos can still be used normally. 
  If both Monsters are in the same city at the end of the game, Tickets that include this city are only halved (not halved twice).
  If the two Monsters are in the two cities named on a Ticket, this Ticket is only halved (not halved twice). 
  When you move a Monster, you must move him at least one space, you cannot retrace steps (as in moving one city forward and then one city back), and you may not end the Monster's movement in the same city where it started the move (by moving in a loop).