ESTA then F1 Visa (via Mexico)

I am a New Zealander and 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 an ESTA ~70days 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).
  4. Fly Mexico-US, enter on my F1 visa.

My main questions are:

  • Will there be any issues entering initially on my ESTA, with an F1 visa in my passport.
  • Will there be issues flying to/from Mexico? I see from other posts
    that technically you must go further than Canada, Mexico or nearby
    Caribbean Islands but it is not consistently enforced. Should I look further afield, maybe Costa Rica?
  • I know that travel to Canada/Mexico counts as part of the 90 day ESTA limit, so will the days keep on accumulating once I re-enter on the F1, eventually exceeding the 90 days and causing problems?
  • Will I be able to re-enter the US after only ~2days in Mexico?

Any advice would be much appreciated! Thanks 🙂