WRT b: surely using fuel that is above the engine will bring the centre of mass down, because the engine's mass is still there with less fuel mass above it?

Unless the rest of the vehicle's mass (all the other equipment, and crew if it is a manned mission) has more mass than the engine & landing apparatus of course, which I think (caveat: no deep thinking involved here) is likely for manned missions but less so for others? I'm assuming the mission mass is above the fuel (having the fuel on top would presumably be less safe/reliable/practical/other).