It seems that by 'application' you mean an application for the UK visa
From the experience of people I know, the success there really depends on how the supporting documents are prepared - and it seems that you might need some extra work there.
1. Should be OK - the date when the bank statement was issued should be not earlier than a month.
2. They require originals (the documents issued by your uni) + one copy, and in addition, if the original is not in English, a certified translation.
3. All fees you should pay are included in the visa application fee (except for delivery, I guess, if you choose to order it).
4. When you filled out the online form, you were required to print a copy of it, and also print out and fill in a copy of, AFAIK, Appendix 8 (for General Student Visa). All these should be taken to the visa centre.
5. Really don't know what to say - when I was preparing a visitor visa, I brought the copy of my old passport just in case. But I also knew of people who just gave the number of the old passport and that's it (they didn't make a copy of it in advance, and in my country, when the new passport is issued, the authorities take away the old one).
Hope this helps - and good luck!