I am a FP physician.
It is tabulated and they see the progress note so they can verify if you completed the required elements for that level of billing. Whether the particular provider actually tabulates what questions they ask or just document that "safety screening performed" is an individual decision, although if they don't specifically list what was reviewed they may get gigged for "inadequate documentation" and not be compensated for it. A lot of this is medicolegal- if you don't say that someone should lock their guns up, its not beyond the realm of possibility to get sued that you didn't cover this when someone has a bad outcome... Now I highly doubt that the lawsuit would win, but people do it over similarly asinine issues, and if its documented, the plaintiff's attorney will drop the case rather than go to court in the hope that the insurance company will hand over a amount of money that will cost less than defending the case would cost.
I'm not sure how much the insurance companies actually retain, but they do get essentially all the information that the doctor documented to ascertain that there is no "fraud" going on. They DO retain the diagnosis codes, and this can come back to impact you when you buy insurance.
You would be surprised how much mickey mouse back and forth goes on in the business office of any practice.
As I'm sure you know, once something is in electronic format and sent somewhere, it never truly is destroyed.