They only affect your score for 6 months. If inquiries are significantly dropping your credit score, it means you have a very thin file. I think I averaged 90 inquiries a year the last 5 years and I sit promptly above 720 year round. You need to diversify your lines of credit to stabilize your score. No fee credit cards and a mortgage are the best ways to do that so long as you don't carry a balance on your credit cards. An individual inquiry more than likely indicates that you are applying for an individual line of credit ie. no additional applicant was applying with you on that loan.

The dealer didn't pull your credit 7 times. They pulled your score once and sent your application to 6 lenders. Standard practice. It's called shotguning.

There are 3 major reporting bureaus. Experian, Equifax, and Transunion. All of them use different algorithms for different models. You have hundreds of compiled credit scores. Your Auto score will be different from you Bank Card and Mortgage scores and all of those will be different than you standard model score as well. They take all of the line items in your bureau and calculate a risk score based on those factors with different equations.