Can you use a mode 3AC interrogator in EU airspace?
Partial answer:


  Is the backwards compatibility seamless and simultaneous?


Yes.


  Able to reply to both mode S and mode 3 interrogators in real time? 


Yes.


  Or a toggle switch between modes, in which when mode S is selected mode 3 interrogations will be ignored?


No - a Mode S transponder will respond to interrogations by a "pure" mode 3 interrogator. Mode S interrogators have a special interrogation format that allows them to interrogate "pure" mode 3 transponders without triggering replies from mode S transponders even though those transponders do support mode 3 interrogations.


  Do European standards allow mode 3A/C interrogators to operate within their airspace?


Don't know.


  Could this cause interference with local mode S infrastructure?


Yes, in principle, for the same reason (FRUIT) that mode S was introduced in the first place - "overcrowding" of the airwaves. It won't be catastrophic. There are already plenty of airborne mode 3 interrogators operating (TCAS and AWACS).


  Are there any other potential concerns with operating a mode 3 interrogator in EU airspace?


Consider both radio communication regulations and aviation regulations.