An ability that triggers "whenever you firebend" triggers whenever a firebending ability you control resolves.

Mana from firebending abilities isn't lost until you leave combat and go to your second main phase. It can be used at any time during combat, even after combat damage has been dealt.

Multiple instances of firebending on the same creature trigger separately, each granting you the appropriate amount of mana.

Firebending abilities aren't mana abilities. They use the stack and can be responded to.

To determine the total cost of a spell, start with the mana cost or alternative cost you're paying, add any cost increases, then apply any cost reductions. The mana value of the spell remains unchanged, no matter what the total cost to cast it was.

An ability that triggers "whenever you earthbend" triggers immediately after the list of actions earthbend entails is complete, even if some or all of those actions were impossible, perhaps because an effect does not allow counters to be placed on creatures you control.

Any other mana you add during combat will still be lost as normal when moving between steps of combat.

An ability that triggers "whenever you airbend" triggers after the process described by the airbend keyword action is complete, even if some or all of the actions were impossible.

"Firebending N" is a keyword that represents the ability "Whenever this creature attacks, add N {R}. Until end of combat, you don't lose this mana as steps end."

Avatar Aang's last ability looks at the whole turn when determining whether or not Avatar Aang should transform, not just actions you've taken since he entered or came under your control. For example, say you airbend, waterbend, and earthbend, then play Avatar Aang. If you firebend later in the turn, then when Avatar Aang's ability resolves, he'll transform since you've done all four this turn.

An ability that triggers "whenever you waterbend" triggers whenever you pay a waterbend cost, regardless of how you paid that cost. You do not have to tap artifacts or creatures to help pay the cost for the ability to trigger.