I use a custom built Manson electric fitted with a Shadow synth guitar pickup as a bridge nut. I connect to Logic or Mainstage via a Roland GI-20 MIDI interface for guitar synths. The acoustic part of the signal is fed in via a MOTU 828. I use an Evolution UC-33 as a MIDI controller for both Logic & MainStage. I have had no trouble controlling six or more synths simultaneously at the same time as playing natural guitar sounds. Not recommended as the sound can get very muddy in a short time, but it can be dnoe.
To answer your questions:
1 Yes, MainStage should recognise your controllers with no difficulty. Read the manual section on assigning synth controllers. It is very simple to do.
2 You can assign any of Logics synths to your guitar. Some will be more effective than others, but they will all work.
3 By amp modeler, I assume you mean the Guitar Amp Pro plug-in. Yes, it will work both for guitar & for your synth patches.
Godin guitars give a very good signal. I haven't used one with MainStage, but I was very impressed when I ran one through Logic 7. I would buy one, but the fingerboard is too narrow for me, I trained as a classical guitarist & a lutenist. My electric has a classical width fingerboard.
Enjoy the world of MIDI guitar!