There is a writing component in DAP 1 - we may have different definitions of essay. I am not sure how it will differ now that the interview is online, but it will still be there.
I am not sure how many applicants advance from DAP 1 to DAP 2, but after DAP 2, about 25 finalists are paired with each partner college. While Posse will try and make sure that students are paired with one of their 3 choices, their primary selection criteria are fit (my kid was paired with her 2nd choice, which was indeed a better fit than her first choice).
The students then decide whether they are willing to apply ED1 to the college with which they are paired (some don’t).
In DAP 3 interviews 10 (sometimes 11) finalists are chosen as Posse Scholars. Finalists who are not chosen are added to the Posse Access list, which increases their chances to be accepted RD to Posse college partners.