Is it reasonable to suggest a PhD thesis topic in an interdisciplinary area in which none of the faculty members specialize?
Well, no answer yet? I'll give it a try, even though I'm in CS and I'm residing in Europe. But maybe it helps a bit:

To adress your questions 1-3:


In CS it would - in math it depends on the will of the supervisor. 
Depends on your PhD program and supervisor. It might depend who is sponsoring the PhD program as well. 
I don't know enough about the US system to answer this one - but you asked for an other option and there is one: 
Just quit the program you are in and look for an other one in a CS department! Sounds a bit disruptive, but if this is your research interest, you should follow it!