Just Cause 2 – Can a Detached Mounted Gun Be Carried with a Car in Just Cause 2?

Yes, the planes will keep taking off while the location has not been completed, but once you complete it, they stop.

This is actually an issue with the game that can prevent 100% completion. There is at least one jet type that can only spawn in the "taking off" mode, so if you inadvertently complete all the locations where it can spawn without hijacking that jet type, you will never have another opportunity.

You either pick it up from Soldiers dropping that weapon or just rebuy the Weapon from the Black Market. When you touch it's case, it just refills your ammo if you have that weapon equipped.

There are also weapon stashes around military bases where you can replenish for free.

There is no way to obtain Ammo for Weapons introduced by DLC's outside the Black Market since NPC do not use them.

There are some Mods around which give you unlimited ammo etc, but you have to decide yourself if you want those.