Proofs of paid ancillary costs

Do I have to prove these already paid items to the bank or will they just accept it?

Depends and no one here can tell you! Only(!) your bank knows ... It is advisable
A) to record all payments (Excel spreadsheet),
B) to file all documents ("invoices") related to them,
C) to always pay by bank transfer,
D) to keep the payment receipt (bank statement).
At some point you will need this ...