Airbend is a keyword action. To airbend a permanent or a spell, you exile it. As long as that card remains exiled, its owner may cast it by paying rather than paying its mana cost. This doesn't change when that card can be cast. If you airbend a creature that an opponent owns during your turn, they'll usually have to wait until their next turn to cast it again.

Firebending is a keyword that always includes a number. Whenever a creature you control with firebending attacks, you add that much red mana. You don't lose this mana during that combat. Any of this mana you still have as combat ends will be lost. You won't have it during your second main phase.

A Saga creature is also a creature and can do everything a creature can do. It can attack, although not the turn it comes under your control. It can block. If it has any abilities or flavor text in addition to its chapter abilities, those abilities and flavor text will be in a separate part of its text box under its type line. Saga creatures aren't on the battlefield for a long time, but they can make a devastating impact in their short time with you.

Exhaust abilities can have all sorts of effects. Not all of them involve +1/+1 counters, and a few of them aren't even on creatures! They usually have an easy way to remember that they've been activated, though, whether that's putting a counter on the permanent with the ability or creating a tricked-out token. If a permanent with an exhaust ability that's already been activated leaves the battlefield and then returns, it's a new object with a new instance of its exhaust ability. That exhaust ability can be activated.