Moving
infantry and weapons teams (guns, mortars, MGs) are more vulnerable to all types of fire. So a rifle section that scoots 6 hexes up a road and gets mortared or machine-gunned is likely to be severely mauled, a section that moved 1 hex much less so. Its easier to hit, easier to suppress and will tend to suffer more casualties if hit than a halted or slow-moving section.
A dismounting element takes the hexes moved of its transport - so barrelling up 15-20 hexes inside a 'pig' and jumping out right in front of a live MG is somewhat suicidal
.. Therefore dismounting of infantry, if it really
has to be done so out in the open, is best to do so at the start of the APC's turn. Otherwise you get the 'bunched target' penalty for any movement the APC made as outlined above. Better yet - dismount in a covered area (in a dip, or screened by smoke or terrain) and later walk forward, with the empty APC following the skirmish line.
Moving vehicles are the converse - less easy to hit the faster they are travelling.
Moving units are less accurate - even stabilised vehicles - especially if the vehicle has exceeded more hexes than its stabiliser value (So if it has stab=2, try to keep movement to 2 or less if shooting). The more hexes travelled, the less accurate the element becomes.
The main advantage of the stabiliser is that it keeps target lock as the vehicle moves, provided it does not lose LOS. The vehicle therefore keeps its place on the ranging ladder and does not have to re-start the ranging sequence all over again post the move. The gun ranging ladder is usually 3 shots to full accuracy - 2 if it has high FC and a laser RF, so in MBT not WW2.
Firing at the short halt is really only possible to simulate, as you say, by firing and then doing any required moving afterwards, or perhaps more by just keeping to a slow movement rate, say 2-3 hexes travelled. Charging a unit its full move - especially down a road - and then popping off the couple of shots left, is more like 'spray and pray'
.
cheers
Andy