Actually I believe contact for movement is determined at the moment of movement, so you always want to move the HQ LAST. If you don't then it "leaves units behind" if they don't have radios and don't have an objective.
Key things to remember - always set formation objectives! click on the unit HQ and use the red flag to set the formation objective.
Recon units DON'T use movement objectives! Click on them twice and a 360 degree movement field will show up.
Units in Defend stance don't move, and if "left behind" can becoe stuck...
Your "0" doesn't function fully if retreated or at all if routed - so make sure they rally first so they don't "waste" their rally attempt on others and stay suppressed themselves.
I will look, but I do not believe there is an experience check to get back in command, but there may be occasional "command failures" where units otherwise in command sometimes become "out", but htat is rare.
THe battlefield is a chaotic place and sometimes your troops don't operate "by the book" that is a problem with the game becasue sometimes when you want to do something and can't its easy to cry "BUG" when it sthe games "random factors" temporarily aligning against you