guess I'm used to the rules, but each Command Card is but a small part of the battle, and the actions are not necessarily a chronological and even amount of time.
There are however certain logistical and physical limits to Ancient combat (and Medieval combat) that we don't necessarily understand from a modern perspective. For a starter, arrow supply is pretty limited, and archers spent time foraging arrows to re-supply. The English army of Crecy fame was a logistical wonder, supplied with 90,000 arrows if I recall. Wikipedia says 72 arrows per man, about a 15 minute supply at maximum rate. Ancient archers carried 20-40 arrows each. Javelins and spears were 2-3 per man.
Melee combat was also quite physically exhausting, and it was reported that frontline troops fought for 5-10 minutes, drew back to recover, fought again, over and over. At least one theory on Roman supremacy was the manipular system that allowed breaks in combat. However, whatever the theories, there is a physical endurance limit, and it is quite short.
So I think what you should consider these issues when thinking on the game.
What is very clear is that the rules allow only ordered units to battle. So in answer to your query;
So if I play a command card ordering my cavalry to move, my archer infantry can't fire, nor can my infantry do close combat with enemy units they are next to?
Correct, the archers cannot fire, and the infantry cannot do close combat.
"I will either find a way, or make one."
attrib to Hannibal Barca