Directly from Square Support:

Square can process internationally-issued cards bearing a Visa, MasterCard, American Express, JCB, Union Pay, or Discover logo.  Please keep in mind that the processing of internationally-issued cards is subject to issuer approval and that the fee per transaction for online-entered transactions are listed here.

Here is a quick video from Square:

Please note that while you can process internationally-issued cards as stated above, you will not be able to use Square if you are located outside of the country in which you activated your Square account.

Regarding your account: with us:

The currency of your platform services needs to match the currency set in your Square account. Therefore, if you offer services in your platform account in other currencies, you will need to change those services to USD before charging your clients for those services.