Yes,that's right.You use them.

Both are common usage.:) I don't think there's any specific corresponding term for 刷卡 in English, 刷卡 means the behavior of having your credit card slide over the machine to pay, whereas the expression that people use in English is more about the procedure to pay.

either is fine.

Both are very common. The only difference between them may be that you cannot say "刷信用卡" when you are talking about paying online by credit card, in which case you don't really swipe(刷) your credit card through a credit card terminal.