Google Play Store – How to Add an App to Wishlist Through Web Play Store

According to the Google payments help page Change your home, business, or billing address and country:

Each payments profile can be associated only with one country due to tax regulations on the payment methods you pay with. You can't change the country for an existing payments profile and need to create a new profile to add another country. Creating a new payments profile in another country does not affect your existing services and subscriptions. They will continue to be paid with the associated payments profile.

If you are moving or traveling to a new country and want to sign up for new services or pay for products in that country, you will have to create a new payments profile.

When you have multiple payments profiles set up with different countries, you have the option to choose the account for payment.

Create a payments profile with a new country

1. Sign in to Settings.
2. Under Payments profile, click the pencil icon next to Country.
3. Click the link to Create new profile from the message that appears.
4. Click Continue from the next message that appears.
5. From the drop-down list, choose the country to associate with the payments profile you're creating.
6. Enter the address information and click Submit.

If I'm not wrong, you must connect your credit card to Google Wallet to use it in the Play store. To remove your credit card from Wallet:

1. Login to your account on Google Wallet.
2. Click Payment Methods on the left side of the page.
3. Click Delete next to the card you would like to remove.