I know that Apple charges fees after accepting the device (a fee for every device sold). Are there any costs associated with enrolling to the Apple MFI program?
You have to purchase a credit review and have your credit approved in order to enroll in the program. That is the only cost to enroll.
Be aware that this is for large companies that intend to sign an NDA, receive Apple confidential information and pay royalties for access to and/or participation in the program.
The credit check is required so that Apple can ensure your company has the financial resources to bear the costs of participating in the program:
From http://mfi.apple.com/faqs :