Anti-Tank squads' purposes are obvious: To destroy tanks and vehicles. However, besides its normal weaknesses that all infantry have, slowness and vulnerability, it has another. It has little strength against other infantry and helicopters, while helicopters and infantry are good against it. Therefore, anti-tank squads should usually be flanked with Infantry Squads and AA units. Like all units, you should take cover when possible.
In all sense, you should not use them to fight infantry directly. You should only do so when you have an element of surprise, or if the enemy is weakened. You can still use them to delay enemy infantry while calling in Tactical Aid.
This is what the unit was created for. No explanation needed. Just note that even with 3 AT Squads, it'll still take 2-3 hits for a heavy tank to go down. This allows the heavy tank just enough time to squish you if you are in the open. However, if hiding in a forest of building, then you will have no trouble. Watch out for the medium tank's special.
Dealing air units with an Anti Tank Squad is not effective as it is not armed with AA Weapons. It can only attack air units with the rifles armed by the two members of the squad and this is a really ineffective way of taking down an Air Unit. If using an Anti-Tank Squad, bring an Infantry Squad with it as they are armed with FGM-92 Stingers and other AA weapons.
This is the easiest role to defeat for the AT squad, because many support vehicles do not have weaponary to attack ground, like the Heavy Anti-Air. They also have weak armor, so 2 shots from 2=3 AT squads should decimiate a Support vehicle. Watch out for artillery, as it can easily hit you, and wipe out your squad. Always be on the move. Remember that support vehicles can also run over infantry.
Usually, if there is a lot of tanks and vehicles, infantry commanders will deploy a lot of AT squads. However, they will deploy some normal Infantry Squads for AA, and sometimes deploy snipers for killing infantry at a far range.