Must all invoices/faktury state a self employed person's NIP or just receipts/paragons?
You have to ask your accountant, but I would say yes. If not, these invoices would be invalid and your taxes will be higher. I suppose you run "działalność gospodarcza". There are different ways for how to pay income tax and in relation to this different kind of documentation you need to have :
1) bases is - "książka przychodów i rozchodów" - percentage of your profit,
2) "karta podatkowa", you pay constant tax -
3) "ryczałt ewidencjonowany" - you pay percentage of what you take - costs are not important
Taxes rules in Poland there are very complicated and very changeable.
And the good and reasonable accountant is the most important you need.