I just negotiated a 2/1 buy down for my client. We were trying to negotiate price, but gave the seller full asking price with a 2% concession. So our net number is lower, but we had to offer a higher purchase price to account for the concession. That concession will fund the buy down, and any leftover balance will go towards closing costs.
So essentially you are just asking the seller for a concession towards closing costs, because discount points are included in the list of approved items that seller concessions can be used for.
One thing to keep in mind is appraisal-- the seller will only give you the full concession/credit IF the property appraises for the inflated number. If it doesn't appraise, it will of course chip away at your concession, or maybe even get rid of it entirely depending. Then you will need to come out of pocket at closing to pay for the buy down yourself, as the seller most likely won't be willing to renegotiate price, just because it didn't appraise for your inflated number. Hope that makes sense!
In terms of your credit pulls, as most buyers 'shop around' for rates, multiple inquiries from different lenders are typically counted as only a single inquiry — as long as they’re made within the same 14 to 45 days.
Best of luck with your purchase!