That assumes the ship's radius is a limiting factor. It isn't if you spin the ship against a counterweight with a tether (the spent third stage which is going with you on the same trajectory more or less).
Yes, especially if you keep half your fuel/water/supplies in that tethered section. Consume at differing rates to shift CG where you want it.
Well, there's no "consume" in terms of matter, stuff isn't thrown overboard. Besides, the food and water (or what they become) is still valuable radiation shielding.
Well, I think the whole point of fuel is you want to throw it overboard :-) ... at high velocity and on fire.
The tethering happens after the upper lift stage is exhausted. It's then spun from a tether for the duration of the trip, then disconnected before the deceleration burn to orbit Mars. There's no mass exchange while the tether is connected.