Hero skills are listed on the data page of each hero, including the cost for the first usage of each skill. Skills can be used repeatedly, but a second use costs 3 times as much as the first. (***Anybody know how much third and subsequent usage costs?***)
Skills can be 'upgraded' by spending skill points to improve their effectiveness / duration etc, but this will incur higher costs for each use.
Currently (v1.7), if a hero is killed while using an air gunner skill (Price's chopper gunner or Ghost's gunship) the player can continue to use the current skill until ammunition is expended.