Programs can contact you as early as Mid-September or so, and you may get some offers in November/December, but unlikely in January or after. What I did was I scheduled the bulk of my interviews in a month (November), then whichever places I heard back a bit later I pushed them to Mid-Late January. Remember that even if a program offers you an interview early, you can push it back to later if it makes it cheaper to travel to certain geographical regions/easier scheduling.
And yea, I think the max you should do is 3 interviews/week, even if they're all in the same state/city. Ideally 2 interviews/week max I'd say.