Can they land on their own, or do they need a pilot?

They need a pilot. It's not an impossible problem to program a computer to land an aircraft. What happens aerodynamically and dynamically are well enough understood. But the big problem is finding the ground. Commercial airports use very sensitive and complicated equipment to provide radio "glide slopes" that can be followed by instruments on the aircraft. That's so that commercial aircraft can carry out scheduled operations even in abysmal weather (i.e., when you can't see the ground). The sort of regularity is not as important to military operations.

And there is actually a big difference in the software required for attitude control and envelope management. That's pretty simple software. But of course approach and landing requires more intelligent software.

Never fear: there is an ongoing research effort to remove the pilot from the fighter cockpit. Pilots aren't necessarily happy about this, but the problem is that aerial combat is approaching the point where the pilot's fragility is an impediment. Airframes are capable of manuevers that would injure the pilot or render him unconscious. The "edge" in future combat may be keeping the pilots on the ground and letting the high-performance aircraft duke it out.