Avatar Aang // Aang, Master of Elements

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.

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

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.