Hey Toney,
First off you should always invoice your clients and sub-contractors. This is normal business behavior and shows you actually are doing business with XYZ person. Behind those invoices you should have a set contract with a set amount of time you working on the project. The person who has hired your firm (even if it's only you) isn't your Employer. Your business is your employer. S/He is a client of you or your firm. So understand the differience. If he is your employer he is responsible for your SS payments, your insurance, etc. You being a self-employed meaning you are.
Okay to billing in foreign currencies. You should open a PayPal or Transferwise Borderless account. Both will provide you was of transfering between currencies and easy invoicing to clients. Tranferwise offers a better exchange rate.
In order to withdraw monies from your credit union will usually cost you $5 + exchange rate per 200 Euros. I would suggest getting an international credit card like the Chase Sapphire with no internaitonal fees. Pay with that when you can and just pay off the card from your local credit union. When you need cash do it sparringly.
Hope this helps. Check out our Grow group. We discuss things exactly like this for Digital Nomads and Expats.
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