ZZP with customer in NL but intermediary in UK

Good afternoon!
I have ZZP, recently signed a contract with a recruiting agency in UKwho acts as a mediator between me and my present customer from the Netherlands... The contract indicates that it was concluded with the agency, but the name of the end client is also written: BV to whom I provide services.
Every month the agency pays me money, which my real client transfers to them for the hours I have worked, and each time it takes out 240 euros from this amount for its services. I do not issue invoices to anyone, I just keep tracking the hours and they do everything themselves. I receive a paid invoice from the UK (salary minus 240 euros, which, by the way, do not appear separately in the invoice, only in the contract).
Do I understand correctly that:

1. Even if they don't need my invoices, do I still have to create them for accounting?
2. In the amount that comes to me is sewn 21% VAT, which should I pay? Even if this is considered as services to the EU country (for now), and not to the Netherlands, then they (client / agency), as I understand it, do not pay any taxes, i.e. I have to pay, right?
3. Since that monthly 240 euros, I cannot make any tax deduction, since this is a service charge for the EU and since no one sends them to me in separate invoices?