ETA: beaten by two good ninja’s.
As to the US:
USAF practice is the back seat has a full set of flight controls. So the back seater can control the airplane. They receive enough training to be able to probably land successfully in benign enough conditions. There are various controls available only in the front cockpit which would make start-up or shutdown or handling malfunctions impossible from the back seat.
The ability to deploy weapons without the back seater varies a lot by aircraft.
In Ye Olden Dayes of the F-4 the pilot could fire the gun (if equipped) or launch an IR missile without help provided the back seater had already configured whichever of those weapons before he dropped dead. If stuff wasn’t set up, the pilot had no ability to shoot. The pilot’s ability to operate the radar was nil, so launching radar-guided missiles was not doable.
Nowadays the F-15E is the only 2-seat USAF tactical jet; everything else is single seat. There’s not much public info on the details of F-15E weapons systems. I’d bet the frontseater could perform air to air combat and fire air to air weapons without backseat help. The backseater could fly (limited by their skill, not by aircraft equippage) without the frontseater. Any of the fancy guided air to ground munitions would need backseater operation to use effectively.
Conversely, USN/USMC practice has always been to not provide flight controls for the backseater. Whether in the now-obsolete F-4 or F-14 days or the current F/A-18 models that use a backseater. If the pilot is incapacitated, the backseater’s response is to promptly eject both of them.
I expect the 2-seat variant of the F/A-18, the -G, is akin to the F-15 in weapons system. IOW, the frontseater can perform air to air combat and defend themselves basically unassisted, but the backseater is essential to do any of their real air to ground or EW mission.
For both F-15E & F/A-18G I’d expect the backseater is a large asset in an air-to-air battle, but is not 100% essential to the basics of shooting.
As to survivability …
Modern fighters are pretty fragile really. The power of modern missiles or cannon fire is such that armoring doesn’t really work. You can’t carry enough to matter.
Back in the day of the F-16, there was one single 4-plex computer that was absolutely essential to keeping it airborne. It wasn’t armored, but they installed it directly under the pilot’s butt. The logic being that any battle damage that got either would get both. By concentrating the most critical components in the smallest possible volume they minimized the aircraft volume that was subject to 1-hit is a kill.