Is it usual to write your terms on the invoice?
Yes, it is called "Termin płatności", and is a standard part of a VAT invoice. But like Seanus said, if your friend is just going down the self employment route he will not be generating Invoices, but bills. (me thinks)
what the typical invoice terms are here e.g. 30 days.
Just from my experience it is typically 7, 10, or 14 days. Which does seem quite short. I don't recall having seen anything longer than 14 days, unlike the typical 30 days I am accustomed to outside of Poland. I don't know if this cultural or part of the accounting standards here.