international travel – Visa Waiver Program-> Mexico -> F1 Visa

I am a New Zealander wanting to clarify some travel plans for next month regarding my F1 visa to alleviate some anxiety!

Current itinerary is:

  1. Fly NZ-US, enter on VWP ~60 days before class starts (with a return ticket) to visit friends/spend time with my partner.
  2. Refund my return ticket once I’ve arrived.
  3. Fly US-Mexico for a weekend ~25 days before class starts (such that I can re-enter on F1).
  4. Fly Mexico-US, enter on F1 visa.

My main questions are:

  • Will there be issues flying to/from Mexico? I see from many other posts
    that technically on the VWP you must not terminate your travel in Canada, Mexico or nearby Islands. Is this relevant? as I will re-enter on a F1 visa, not via the VWP.
  • I know that travel to Canada/Mexico/nearby Islands count as part of the 90 day ESTA limit, so will the days keep on accumulating once I re-enter on the F1 and eventually exceed 90? as I never technically left by this definition.
  • Will I be able to re-enter the US after only ~2days in Mexico?

Any advice would be much appreciated, thanks!