You need to be a little proactive against armor, don't wait around for it to arrive. But if you get a cpt with a zook, you won't need more AT for another 5-6 minutes in most cases. If he goes heavy light vehicles then is the time to get a 2nd or 3rd zook.
For each tank you want an AT gun, and some form of infantry AT (rifle nades, zook, etc.) or a tank of your own. If he makes more tanks than AT guns or tanks you won't be able to focus fire them down faster than he can switch targets.
AT gun crews firing the gun are in green cover, except the rakenten which gets no cover. The other crew members are in whatever cover they find. If you try to place an AT gun in cover what will generally happen is the shot from a tank can miss the crew but impact the cover, when it does this it acts like a grenade thrown on your troops and can kill them. Therefore, leave the crew out of cover but far enough back to prevent them being sniped by infantry. You will probably need to recrew or reinforce AT guns fairly regularly.
The USF mortar scatter is reduced by range and vet. The shorter the range the more accurate the fire. I believe the barrage fires three shots, but you can cancel it anytime. Increasing the rate is on the cooldown the crew should fire at the same rate as normal.
Barrage is usually more accurate than attack ground. Targeting a unit is more accurate than firing blindly. If you can see a unit your scatter on that unit will be reduced by 25%. Which is why if you can dual with infantry the mortar will appear to snipe the squad over and over. If you want to get into the depth of the game, and all these little mechanics, head over to Cruzz's thread at:
https://www.coh2.org/topic/36347/cruzz-s-the-more-you-know
Many of those stats were changed a while ago, but some of the mechanics still exist and plenty of insight into how the game functions. Also make sure to read the patch notes so you can see how things change.