Ya'll be trippin...
Kryptonians were absorbing solar radiation aboard Black Zero, it is very clear. (It should be known, in general, that energy from the sun can penetrate solid objects. It even hits deep below our planet's surface.) They survive getting hit by bulkhead doors as being shot with guns designed to kill them with no damage or visible injury. The female Kryptonian even punches a hole in the cockpit (the gun is what did the real damage, the punch was in the center of the pod, the sparks were coming from the top where the shots were.) Further proof hat kryptonians have superkryptonian abilities aboard their ships when within range of a young star:
This is from Man of Steel's official prequel comic. Kara Zor-El and Dev-Em are fighting aboard the scout ship that Clark finds. They are only approaching Earth at this point but are obviously within the sun's range. They have both begun to absorb solar radiation, and it has given Dev-Em the strength to dent the metal walls of the ship with 1 punch.
Lois overpowering the female soldier was somewhat PIS. The soldier was really trying to get the gun away from her when Lois kicked her. She succeeded but Lois forced separation. This isn't entirely unimaginable as the soldier wouldn't weight so much that Lois couldn't move her, but she still would have been dragged out of that pod if it were me.
As to Kal regaining his strength: As has already been beaten to death, Kryptonian atmosphere inhibits his abilities to an unsurpassed degree because he never adapted to it. All of the solar radiation he had stored in his body was still there, the atmosphere aboard the ship was simply inhibiting his ability to process it into superpowers. Implying that Earth's atmosphere alone can give him superkryptonian abilities is nonsense.
Jax-Ur grabbed his throat because he could likely feel the change, but he ran away because he is a scientist, not a soldier. A nerd not a fighter. I doubt Faora would do the same in his position.