Yes. When you have a critical mass of the documents they ask for, lodged, then you are more or less at first base, and they issue a precaria. In terms of the mechanics, previously you loaded the documents yourself to the system and then they called you in to present the originals in person and if they were satisfied at that point, would issue the precaria. It may still work that way; others can confirm. (I am not touching any of this part in my current process; a lawyer is handling it for me, which is why I can't be sure how it works in practice now.)
You do not apply for the DNI. They issue it to you automatically once your temporary residency as a pensionista is approved.
