#1 The "basics" of base capture, ie the absolute bare minimum that is required (in the Main Arena*) to capture a field is all the buildings and structures in the "town" have to be destroyed and 10 troops have to landed in the map room in the town (the map room is a little mound/bunker looking thingie with a doorway in one side). In the main arena a little more is required, supression of base defenses, all the steps required to make the above possible.
*this is for the main arena, special events, or the Combat Theater sometimes (but not always) have slightly different requirements
#2 I am not sure how resupply works but if you look in the help file on HTC's website or get the downloadable file the resupply system should be explained there.
#3 A squaddie of mine wrote a rather lengthy article on GV's and how to employ them but I don't have the link on me at the moment I will try to post it here tonight when I get home. But here are some basics
M-3 troop carrier, halftrack, good speed, one .50 cal MG on top lightly armored (ie just about anything can kill you).
M-8 Armored car, extremely fast, has one 37mm gun in the turret can kill anything smaller than the Tiger at close range. One .50 cal MG for air defence. Lightly armored
M-16 Halftrack, anti-air platform 4 .50 cal MG's otherwise same pro's and con's as the M-3.
Ostwind or Flak Panzer, German anti-arcraft gun. 37mm cannon in open topped turret on a Panzer IV chasis. More heavily armored than the halftracks but the open turret makes the gun vulnerable to at least .50 MG fire from above (maybe .30 cal, not sure).
Panzer IVH Standard tank in AH. 75mm long barreled gun can kill anything else in the game under the right conditions (ie you gotta get pretty close to kill a Tiger). Decent armor can shrug off MG fire and take several hits from heavier cannon. Tiger will kill you at just about any range, other panzers will depend on where you hit them, or they hit you. 7.7mm MG for air defense
Tiger Heavy tank, comes at a perk point cost. 88mm gun kills anything, period. Heavy armor it is virtually immune to air attack (will take near a direct hit from a 1000lb bomb or more to do anything but damage a track, which will of course immobilize you). Major drawback to the Tiger is it's turret traverse if very slow. 7.7mm MG on turret for air defense.
LVT's amphibious tracked vehicles usually launched from the CV's (aircraft carriers) one is a troop carrier with .50 and .30 cal MG on board the other is a howitzer with a 75mm gun that only fires high explosive rounds (as opposed to Armor Piercing). LVT's are lightly armored. Very slow in the water (~10mph) faster on land.
*edit*
Ok I found the link. The squad that has been hosting the file has been disbanded so I don't know how much longer the link will be viable. But for the time being you can get the Complete Idiots Guide to Ground Warfare in Aces High
here.