Hi @michalzw
Case 1: Invoice as normal as there is no VAT involved in either direction.
Case 2: If the UK is invoicing DE, then there is no VAT present to worry about so invoice as normal.
Where DE is invoicing the UK, it would be best to seek professional advice as there may be different rules in DE regarding this.
Case 3: Please see the following guide: Choosing the right VAT options for your overseas clients and suppliers
I hope this helps, but if you have any further questions, please seek professional advice, you’re welcome to post here and an accountant may help, but we are not professionals.