Are prepaid cards, and gift cards considered a form of money?
Prepaid cards are definitely money by any definition— they are essentially demand deposits. An article from the SF Fed states this clearly:


  In contrast to purchases with credit cards, debit card purchases transfer money electronically from individual and business bank accounts to the sellers’ accounts. Spending with a debit card would affect demand deposits and the money supply in the same way that purchases with a check or cash does. Because a debit card transfers your existing financial assets—the financial assets that you may access with a debit card are included in the money supply.


Gift cards, in contrast, aren't generally considered to be part of the measured money supply, but they are in some sense also a form of money. They can be used as a medium of exchange; they are tied to a broader unit of account, and they're (in a manner that depends significantly on the terms of the gift card) a store of value. Rather than being liabilities of banks, as deposits are, they're liabilities of non-financial firms. As a result, gift cards are not quite as fungible as currency is; as you note, they typically trade at a discount to face value. This isn't terribly unusual for money— money during the free banking period often traded at discounts to its face value, particularly as the distance from the issuing bank increased. One of many discussions of this phenomenon can be found in Gorton (1999).