5 of 6 Removed unecessary religious-like wording to remain religious-neutral.

Are all crew on board a spacecraft trained to handle flight-systems?

Spaceflightnow.com writes to say (Edited to apply my highlights)

"The improvements are rather significant," Kelly said in a NASA interview. "The displays that the cosmonauts and myself ... use to control the vehicle have been upgraded to make flying it easier. It's less operator intensive. But the main and most important change is they have a new, what we would refer to as a flight control computer."

This was in context of the (then) new TMA-M craft which carries a crew of three.

Wikipedia further writes to say about TMA-M

It has an automatic docking system. The ship can be operated automatically, or by a pilot independently of ground control.

In all probability the spacecraft from launch through docking, is controlled by computers. The pilot (or whatever designation applies) is responsible for managing the flight - applying his mind to ensure the flight is nominal, go/no-go decisions. In the absence of dynamic flight surfaces (as in the Space Shuttle) the pilot may, in an emergency, only control the duration & intensity that various rockets fire.

In mind of the cost involved, it seems reasonable to assume the crew must cross-train.

Are all crew on board a space-bound craft (Soyuz, Shenzhou, other craft of that ilk) trained to monitor, and control flight systems in & out of Earth's atmosphere?

For instance, say, an emergency de-orbit or launch abort, or ...

EDIT: The situation was a little different with the STS aka Space Shuttle which was possessed of a true cock-pit with flight-controls. NASA writes about this to say

Landing-5 minutes

The orbiter's velocity eases below the speed of sound about 25 statute miles from the runway. As the orbiter nears the Shuttle Landing Facility, the commander takes manual control, piloting the vehicle to touchdown on one of two ends of the SLF.

Operations in orbit though (dock/undock/maneuver) would still have been computer controlled, and astronaut managed though.