While resolving Savai Thundermane’s triggered ability, you can’t pay {2} more than once to have it deal more damage or gain more life.

If you pay {2} while Savai Thundermane’s triggered ability is resolving, the reflexive triggered ability triggers and will resolve separately. This is different from effects that say “If you do . . .” in that players may take actions after you’ve paid mana but before damage is dealt.

If the target creature is an illegal target by the time Savai Thundermane’s reflexive triggered ability tries to resolve, the ability won’t resolve. You won’t gain 2 life.

You can pay {2} even if Savai Thundermane leaves the battlefield before its triggered ability resolves. The reflexive triggered ability will still trigger if you do.

Some cards with cycling have an ability that triggers when you cycle them, and some cards have an ability that triggers whenever you cycle any card. These triggered abilities resolve before you draw from the cycling ability.

Triggered abilities from cycling a card and the cycling ability itself aren’t spells. Effects that interact with spells (such as that of Cancel) won’t affect them.

You can cycle a card even if it has a triggered ability from cycling that won’t have a legal target. This is because the cycling ability and the triggered ability are separate. This also means that if either ability is countered (with Disallow, for example), the other ability will still resolve.