Credit Report: Typically, it costs under $50 to check your credit. With your permission the lender will order a review of your outstanding loans and your repayment history from a third party credit agency. Just remember that every time your credit report is pulled, it shows up on your credit report so do so sparingly.
Application / Processing Fee: This cost, typically a few hundred dollars, is charged to cover the lender's work to evaluate your ability to repay the loan. Some lenders will credit this back to you upon closing.