So in this map, drones are used by all players. Problem is that only specific players can upgrade zerg units. And for balance, I need drones to have +0 Armor like +0 Weapon upgrades. How can I do this?

You can't set the amount of upgrades per unit

Thank you for reminding me?

Anyways, in more detail. All units can be set to +whatever number damage when upgraded, including 0.
(Example)Marine damage is 5 +5 per upgrade
Can this be done with armor? As it seems to be set as default x+1. But I have seen a unit with x+0 armor.

Nope, I think the only thing you could use for this is EUD Actions, but that's a bit over the bridge.

Strange, I swear I saw a map were regardless of how many upgrades of armor you had, your civilian's armor wouldn't increase. Oh well, thanks.

Armor upgrades are always +1 armor per up. If any particular unit is excluded from getting armor upgrades, such as the civilian you mention, then it'll only affect that unit type, and there isn't any way to transfer that property to other units.

Note that the ultralisk can get an additional 2 armor from their special upgrade, and this is applied as 2 +1 armor upgrades (so their box says 5 if they have the +2 armor and +3 regular ups).