In Hero Academy, if I lose one of my units and step over him in the next turn (so I save him), do I also save any equipment he's carrying? Or, is the equipment lost, but the hero is saved?
Stepping over a unit that is "knocked out" does nothing to the unit. When a unit is "knocked out" they retain all their power-ups and equipment. If they are revived on that turn, there is no loss at all. If they are not revived on that turn, the unit and all of their equipment is lost.
Reviving is different for each race of heroes. For example, in the case of Team Fortress, a
respawn token may be considered a "revive", but it actually resets the hero and places it back on the rack. All power ups are removed in that case.
The only offensive bonus I know of given for a downed unit is for the "Tribe" race. When one of their units is "stomped" by the other team, every "Tribe" hero is given an offensive bonus.