Before my car purchase, what is the general rule on how it affects your credit score if I want to shop around to 3-4 banks/credit unions for an auto loan? TIA
Each credit pull will be present on your reports for the next 2 years.
Most credit only looks at inquiries from the last 12 months.
As far a having all pulls for the same purpose, that should be 30 days. SO if all of the HPs code as Auto Finance, for scoring purposes 15 pulls should only count against your score as one HP. The thing that can happen is not all HPs may say auto financing.
You are certainly on the correct track to get pre-approval for financing.
If a future credit decsion gets flagged for too many inquiries they can likely do a manual review of your credit to see that all the inquiries were for auto purposes.
If you think PenFed would approve you, you can do the 1 EQ HP to apply for membership, checking, LOC, CC and an auto loan. This assumes you are looking for some additional products and would qualify.
Hopefully I answered your question.