Is there such a thing as a no-cost or no-fee loan?

Not really.
While some lenders occassionally promote "no-cost" loans, banking regulators have cracked down on these misrepresentations.
Advertised "no-fee" loans may actually cost the borrower more over the long term because these costs are often rolled into the new note through higher interest or more principal.
A typical no-fee loan is one where the points charged and all fees are included in the loan principal, meaning that the borrower does not pay these expenses at the close of escrow, but instead ends up paying on them over the life of the loan. The loan is called a no-feeloan because the borrower is not charged any fees up front.