Julie here from Shopify Support.
To clarify, are you currently using Shopify Payments? If so, your payout currency must be the same as your local currency, even if you are selling in USD. There are a couple of exceptions, however — Canadian merchants have the option of getting paid in either USD or CAD, while Swedish merchants can choose to be paid in either SEK or EUR.
We actually have a help doc on selling and getting paid in different currencies that offers further clarity on how this works. This help doc also includes a chart that outlines the available payout currencies for each country where Shopify Payments is available. In your case, it's safe to say that you'll be receiving payouts in EUR, rather than USD.
As for currency exchange and conversion fees, these are always applied when a payment is captured or a refund is issued. The currency conversion rate is based on current market exchange rates and is automatically updated whenever the rate changes.
The currency conversion fee, on the other hand, is the fee that Shopify charges to convert currencies for your payouts. This fee is based on where you're located and you can find out what your conversion fee is by heading over to the Conversion rate and fee section in our help doc on Shopify Payments processing and conversion fees. You can also see your currency conversion rates and fees for each order in your payout details over in Settings > Payments > View payouts > Transactions. Because the conversion is handled by Shopify, you won't need to pay a conversion fee to your bank. Your bank may charge you a deposit fee, though, so it might be worth reaching out to them to confirm if this is the case.
If you are using a third-party payment gateway, however, you'll just need to check with them directly to find out which payout currencies they support.
I hope this clears things up, but let me know if you have any further questions!