Maybe. Paying off your student loans might help reduce your debt to income ratio allowing you to qualify for a higher loan amount. However, paying off installemnt debts like student loans and car loans might lower your credit score.
It depends upon when your hard credit report was pulled. Most lenders require a mortgage to close within 120 days of the credit report being pulled for that report to be used.
Yes, you can always cancel a refinance application up until closing. A cancellation might result in paying third-party fees, but the right to cancel is available. In certain situations, you can cancel your refinance application up until 3 days after closing.