If Finder of Paths Unseen causes Heart of the Wildfire to place Presence, destroying Invaders, does Finder need to pay for Responsibilities to the Dead? What if Finder destroys some of Volcano's Presence?

If Finder of Paths Unseen causes Heart of the Wildfire to place Presence, destroying Invaders, does Finder need to pay for Responsibilities to the Dead? What if Finder destroys some of Volcano's Presence?

No for Wildfire. Yes for Volcano, assuming the damage from destroying Volcano's Presence destroys 1 or more Invaders/Dahan.
When placing Wildfire's Presence, Finder's action itself did not cause any destruction. It "directly triggers" the destruction (via Wildfire's special rule), but it did so by adding Presence, not by moving Dahan or Invaders. (Earlier printings of Wildfire incorrectly said "when" instead of "after" for the Special Rule; see the errata / clarifications on triggered actions.)
Collapse in a Blast of Lava and Steam is phrased as a modifier - when Volcano's Presence is destroyed, it modifies the current action to also do 1 Damage. If that action is Finder's, it's Finder dealing the damage. (This would have worked more thematically if Collapse in a Blast of Lava and Steam had been a triggered action, since then it would have been Volcano dealing the damage.)