This is just my understanding, so take it with a grain of salt.
Does standard equipment listed on the vehicles count as used modification slots?
From my analysis of drones and vehicles that start with standard equipment, standard equipment is already included, and the mod slots available are the slots that remain *after* standard equipment (which occasionally means that some vehicles and drones may have started with extra slots). This is why many drones and vehicles start with fewer slots than their body would normally suggest.
Why do the rules on vehicle modification for armor tell us that the maximum you can add would be equal to BOD when you need at least Rating*2 in modslots?
So technically while being allowed to increase vehicle armor by the value of its BOD, the technical maximum is BOD/2 for standard armor. Which makes most vehicles worse in soaking damage than mil-spec armor.
Why has personal armor become more efficient than vehicle armor?
The maximum is actually (Vehicle's base armor) + (Bod / 2). Vehicle mods are aftermarket add-ons, and modify the existing vehicle, so any vehicle armor you add is in addition to what comes standard on there. This typically means that vehicles can have very high armor ratings -- like the Dodge Rhino, with its base 14 armor and 24 body, can theoretically be modified to carry a whopping 36 armor.
And the phrasing of "The most armor any vehicle can add is equal to vehicle Body" means that if for whatever reason you managed to get a vehicle with a lot of extra mod slots, you could not add more additional armor to the vehicle than equal to the vehicle's body (so a Bod 3 vehicle with +3 additional mod slots could still only have +3 armor added to it). It sounds unlikely, but this ruling covers their bases in case someone adds a very mod-able vehicle later on that could theoretically break this rule.