If you want to run a(n online) business, you will have taxes to do and paperwork to keep up with. No single payment provider will take that away from you, you just need to pay a bookkeeper for that.
Also:
> I don't think that Stripe offers that the customer buys the product from them and Stripe buys it from you?
I have no idea what you mean with this, sorry.
> Does stripe handle the invoicing? So that every customer gets an invoice they can use in their country?
Yes, Stripe does invoicing. How else are you going to book it into your own administration?