How should I wire my pool heat pump?
From what you have described, I see no reason why you would not have adequate space in your sub panel.

As far as wiring, you are correct in that you will have two hots (L1, L2), a ground, and no neutral.

Without seeing the spec sheet for exact numbers, I can only suggest that you take the conservative approach and wire using a double-pole 30A breaker with #10 wire. If you are using some sort of conduit then THHN will be fine, as you suggested.

Note that the NEC also defines rules for supporting conduit and whips. There is no way to answer this without knowing more about the physical setup and distances between your heat pump and sub panel.