Can I buy a plane ticket from a Swedish online travel agency with a US credit card?
Or a US American Express credit card?
If yes, any idea about the fee?
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Unless the online agency's card processor prohibits them from accepting credit cards from outside Sweden, there should be no issue with using your card. These days most online businesses accept cards from around the world, but occasionally you find a business with restrictions.
As to the fee, you need to contact your bank or card issuer and ask what their foreign transaction fees are. There is no universal fee structure, each bank sets their own charges. Some banks may claim no fees, but they get you with poorer exchange rates. ALL banks are in business for one reason, to make a profit.