The last ability of Firesong and Sunspeaker can't target a planeswalker or battle.

A spell causes you to gain life if its cost or effect instructs you to gain life or if an instruction in its cost or effect is modified by a replacement effect and the modified event includes you gaining life. If a spell's cost or effect instructs a source with lifelink you control to deal damage, that spell causes that life gain as well.

If a white instant or sorcery spell you don't control causes you to gain life, Firesong and Sunspeaker's last ability triggers.

If you gain an amount of life "for each" of something, that life is gained as one event and Firesong and Sunspeaker's last ability triggers only once.

If a source you control with lifelink deals damage to you, you gain and lose that much life simultaneously. Your life total doesn't change.

If a red and white spell you control deals damage to multiple things using the word "deals" only once, Firesong and Sunspeaker's last ability triggers only once. Similarly, if a red and white spell's effect causes it to deal damage to one thing and then deal more damage with a second instance of the word "deals," Firesong and Sunspeaker's last ability triggers twice, and so on.

If a red and white spell you control deals damage and also instructs you to gain life, Firesong and Sunspeaker's last ability triggers twice.

Firesong and Sunspeaker's last ability doesn't trigger if a triggered ability of a white instant or sorcery spell or card causes you to gain life, such as the triggered ability of Renewed Faith when it's cycled.