Credit cards. Outdoor rewards.

[Jigger]

Can someone explain to me how credit cards work in general? My wife and I were discussing this and neither one of us are certain. For example, I signed up for the Bass Pro Shop Outdoor Rewards card. We both have one and we put gasoline and other purchases on it. It is a no interest (if you pay within 30 days, I think) and no annual fee. The more we charge, the more "rewards points" we get to use toward purchases at BPS. I ordered a couple of hundred bucks worth of gear from BPS a few days ago and the lady said I could deduct $65 from the purchase price because of "rewards points". I was pleasantly surprised because we haven't had the card that long.

Now for the questions:
1.In general, how do credit cards work? How does say, Visa, make its money? Interest, I know is one way but does Visa also charge a fee to the merchant or does Visa pay a fee to the merchant when the card is used.
2.What does BPS get from the deal that induces them to give me "rewards points".
3.Who is benefitting from our transactions when we pay no interest since we always pay within the 30 day period and we pay no annual fee??

Thanks for educating me.