Transformative Sacrifice

Can the Intensify Aspect strengthen a Bargain by spending Moon to Remove more Presence from the island? How about from a Presence track?
No and no. The efficacy of a Bargain is based on the number of times it has been made, not the number of Presence it has removed, and Intensify can't increase the number of Presence removed from a Presence track.
However, Intensify can strengthen Transformative Sacrifice by removing a 4th Presence from the island (in a land where the Power was already removing Presence) to take and play an additional card, since that power explicitly scales with the number of removed Presence.
Tags: Bargain, Bargains of Power and Protection, Bargain of Coursing Paths, Transformative Sacrifice, 1 more...
Can the Intensify Aspect spend Moon to increase the amount of [thing not on the island] removed by an Action?
No, Intensify can only affect the number of pieces removed from the island by the Remove keyword. It has no effect on actions that remove pieces from other locations (e.g., removing Presence from Presence tracks with Bargains or Transformative Sacrifice ).
Tags: Remove, Bargain, Transformative Sacrifice, Intensify Aspect (Shifting Memory of Ages), 2 more...

When an effect lets you play a card, does that count against your allowed number of card plays?
No. The number of card plays on your Presence track only affects how many cards you can play as part of the "Play and Pay For Power Cards" action in the Spirit Phase. Cards played any other way (usually in the Fast Phase when instructed to do so by a Power) are in addition to those limits.
(Discussion elsewhere) Tags: Playing Power Cards, Spur on with Words of Fire, Unlock the Gates of Deepest Power, Gift of the Primordial Deeps (Serpent Slumbering Beneath the Island), 14 more...

When using Transformative Sacrifice with threshold, what's the maximum number of Minor Powers that Target Spirit can Take and Play?
Four: three from the base effect and one from the threshold.
The Presence removed from the Presence track doesn't double-count.
Tags: Transformative Sacrifice
If you target yourself with Transformative Sacrifice, do your new Powers help you hit the threshold?
No, the threshold is checked before taking any cards, much less playing them and getting their Elements.
Tags: Elements, Timing, Transformative Sacrifice