Your frame should have plenty of clearance for 35mm tires, and they would be better for offroad.
Regarding the BB7 vs BB5, I'd of a mixed mind here. The BB7's are definitely better than BB5's, but they aren't the pick-of-the-litter among drop bar disc brakes like they used to be. When you're riding downhill offroad traction is typically the limiting factor in your braking power. You might find that all the BB7's do is let you get into a skid faster. On the other hand, they are easier to keep adjusted.