When playing Red Pyke, and choosing to have him enter with his +2 might bonus, is there a window where he can be gusted? If so, does it still cost the additional red power?

Yes, there is a window to Gust Pyke after he's played from Hidden, and yes, the additional [C] (red power) is still paid.

Here's the sequence:

1. Your opponent plays Pyke from Hidden. They choose to pay the optional [C] cost. The cost is paid during the Pay Costs step of playing the card — Pyke enters the battlefield with 2 Might, and the [C] has already been spent.
2. Pyke's triggered ability ("When you play me, if you paid the additional cost, ready me and give me +2") is placed on the Chain as a Pending Item.
3. Because there's an item on the Chain, the game state is Closed — this creates a window to play Reaction-speed cards.
4. You play Gust targeting Pyke. At this moment Pyke is still at his base 2 Might, so he's a legal target.
5. LIFO applies: Gust resolves first, returning Pyke to hand. Then Pyke's trigger resolves but does nothing — he's no longer on the battlefield.

The [C] still costs. The additional cost was paid in Step 4 of playing the card, before the trigger ever went on the Chain (Rules 356.2.b, 357.2). That payment is already consumed and doesn't get refunded if Pyke is subsequently removed. (FAQ #10539, #11017, #11295)