Hi,
 
you get the money in USD. That money needs to be converted to EUR, as German tax authorities do not operate on USDs. Usually your bank account will be quoted in EURs, so when you transfer money from PayPal to your bank account you'll get EURs. Now the money is in your bank account (minus some fees that PayPal/Your Bank) collect. In your tax statement you will have to account for all of this, which is somewhat complicated in German tax law. 
 
First up, you will need a tax number. No way around this. This means you will have to file a commercial registration (Gewerbeanmeldung) and then request a European tax number (Umsatzsteuer-ID).
 
Regarding VAT - you will be paid by Unity ApS in Copenhagen so this is a transfer according to §13b USTG (aka. reverse charge). You are selling something to Unity (a company inside Europe) via reverse charge, so Unity will have to pay VAT for that in Denmark (which they will promptly deduct, as it is a company-company transaction). You need to make note of this in your sales tax statement (which you need to provide monthly, quarterly or yearly depending on the size and legal form of your company, to the tax authorities). Also you are required to send a "Zusammenfassende Meldung" to the "Bundeszentralamt für Steuern" every quarter where you state how much you sold to Unity and specify their TaxID (DK30719913). 
 
Finally at the end of the year you need to create a tax statement for your company, where you state your incomes and expenses and then pay taxes on your profits from selling. Depending on the legal form of your company there may be additional paperwork involved (e.g. GbRs need to file a "Einheitliche und gesonderte Gewinnfeststellung", other legal forms may need other documents).
 
All in all this is a pretty complicated thing to pull off from scratch, so I would strongly suggest you consult a tax consultant to walk you through this, as there are a lot of mistakes to be made. You can definitely work this out without a tax consultant, (we do) but having a kickoff round with a tax consultant (we did have one!) goes a long way in not getting any issues with german tax authorities (you really don't want that ;).
 
Kind regards,
Jan

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