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This is not a bug in the game; it’s designed this way. The tent has 3 actions per battle, and the cart has no effect on the tent. Only the skill “Machine Management” affects the tent. Without the skill, the tent can heal 10 HP; with the basic skill, it heals 20 HP and can revive creatures in the squad (up to 20 HP, but it cannot revive a completely destroyed squad). A more developed skill allows it to heal 50 HP and revive the squad. And a master skill heals 100 HP and allows for revival. However, it still cannot revive squads that are completely destroyed, only those where some creatures were killed but not all. The “Tent Mastery” skill also allows it to remove dark magic buffs up to level 3, depending on the skill level. At the master level, the tent can remove all harmful buffs up to level 4.
This is in relation to Heroes V. As for fixing the tent with mods, I don’t know how to do that.