So, lets say you have three openings. You get AP for each of them plus 20 AP just for fun.

As you fill slots you lose the AP for those slots.

Lets say you fill all three openings in the first cycle - but are worried about EEs who you may have to address in the 2nd recruiting cycle.

Do you continue to have the 20 AP available for the rest of the first cycle even after filling your slots?

Good question, I would also be interested in knowing this.

Yes, you do. They may also be useful if you rescind a scholarship.

Yes. Even if you have 0 openings, you'll always get the baseline APs for the entirety of the recruiting periods.