At fast food places, I can use mine at McDonalds, Taco Bell, Burger King, and Wendy's.
Merchants that take American Express will display the logo, usually on their door
Yes, they do. You have to open a Certificate of Deposit and pledge it as collateral. The limit on the credit card is equal to the amount of the CD you open.
Yes, there is a BlueCash line of cards that include this reward. There is no annual fee and the cash back percentage varies depending on the purchase category.