As a merchant, how much of a percentage will the credit card companies keep of each sale?

It depends on the deal that you work out with the company you choose.

That depends on the market. Is there even a market in them? I see Visa and MasterCard and not much else. I know that American express charges more than many merchants are willing to pay so many don’t take it. Only a market can determine a price. The companies will set them and if they don’t work they will change them until they do.
Then after the card company has the money the tax man takes all he can of it. If the price in the market can not be made high enough to pay him the company goes broke.