attach products

You can use the link provided in the "add to cart HTML link" for your buttons so that the product will be automatically added to the cart and your users directed to the checkout.

If the price of your products are in dollar but that your main currency is euros (in the config under the main tab), the system will convert the prices to the other currency. Then, based on the options in your configuration, it will display both prices or not.
So you should change the main currency (don't forget to logout/login after the change so that you can see your modification on the front end).

The country/state fields default value can be changed via the menu Display->Custom fields.

It's not possible to display your products image there. You can edit the the file cart of the view checkout via the menu Display->Views to add your product image, but that require some coding skills.

Could you edit that custom field and make a screenshot of its options ?

In the "zone" option, you set it to display states. You should set it to display "countries" and save. That should fix the problem.