Like a lot of things, credit scores don't always make sense. When a lender, whether that be auto finance, home mortgage, retail credit, or whatever, pulls a credit report, they almost always request a score on you as well - commonly referred to as a FICO score. Many also now have their own decisioning software to produce their own scores. The Fair Isaac , or FICO, model was the mother of this "invention".
Scores range from the "don't have a prayer" level - say below 620 - to the "you can have anything you want" level - say 800 (though the upper limit is theoretically 900).
Yes - inquiries affect your score negatively. Since those making the most inquiries are typically shopping credit hard and fast, hoping someone - anyone - will approve them, the creditors associate such behavior with risk. However, after much public outcry, a couple of key changes have been made.
There are two basic inquiry types: soft and hard. Soft inquiries are you pulling your report, or an existing creditor of yours just checking to make sure your creditworthiness is still OK overall. A hard inquiry is associated with you making application for credit.
Soft inquiries no longer impact your score. Multiple hard inquiries are what can hurt you. But the second improvement they made in the last few years was to add something called de-duping logic (eliminating duplication). This logic will allow multiple inquiries made in a short period - 14 days to 30 days usually - for a particular purchase - specifically an auto loan or a home mortgage - to count as one inquiry. But if you shop credit slowly, and your inquiries move outside of this de-duping window, your score will be penalized. I might also add that there is no de-duping logic I'm aware of for other types of credit application - credit cards, retail credit, insurance, etc.
How much it affects your score is a mystery as the formulas for scores are highly proprietary and very hush-hush. But it doesn't take much to throw you into a bracket causing a higher interest rate on your loan or credit line.
Also of interest is the genre-adjusted score. For instance, an auto-adjusted score. So if you in general are a slow payer but ALWAYS pay your auto loan on time, points are added to your otherwise lackluster score to reflect your implied risk in an auto loan situation. I know they do this for home and auto, but I'm not sure if it is adjusted for other types of credit.
As for multiple cards. What that represents to a potential creditor is untapped risk. If you have 10 credit cards, each with a limit of (for example) $5,000, to a potential creditor you have $50,000 of debt because at any moment, you could create exactly that. So they view your ability to repay as if you have maxed out each line of credit. You may get the loan, but you won't get the best rate.
Aren't you sorry you asked? I think Fair Isaac has their own website now, but certainly if you key in "Fair Isaac" in google or some such, you should find out more than you ever wanted to know..