Other things people have done is ATM withdrawal and using the paper receipt as part of background, or other receipt with enough info to satisfy time and location.
Applications are accepted upon payment. Approvals are a different matter. Additional documents can be submitted the same day they are requested, you have about 14 days to respond with additional documents before your dormant application is voided.
You can rent a place for as long as you want on any Visa. That said, you're under no pressure to move into a permanent accomodation for your extension. If you have everything in place your extension is not going to be denied.