Do I get an invoice sent to my home when I buy a game in the XBox / Microsoft Store?

I really want to know.

No, not really, rather via email

No, just a confirmation by e-mail

Via email, however, you can then think of printing them out as a PDF.

As the users before me have already correctly described, you will only receive a confirmation email. In principle, nothing will be sent to you by post, unless you buy something from the Xbox Microsoft Store.

You can get proof of purchase in many online shops, e.g. With Playstation, Steam, Epic Games, etc. But these are actually always sent as email.