You don't have a choice. You pay the store in Euros (if they are a Euro country, we're not for example). When you receive your credit card statement then your CC provider will have made the conversion to dollars. It will likely be a few dollars more than any online conversion you look up due to exchange rate fluctuations and processing fees when buying in another currency but there will still be quite a saving.
VAT is included in the price as advertised.
As for your refund, allow a few weeks although I'm not sure how you're going to get the refund if you're not the one in Germany?
If you pay by creditcard, you will be able to choose if you wish to pay by your own currency or the currency in the country you're in.