Will the FDIC offer a discount to buy out a note from a failed bank? How much? How long does it take?

It is possible to purchase portfolios of failed notes. They are discounted and pricing depends on the quality, the geographic location of the properties involved, the seasoning of the note. Timing depends largely on the relationship & communication between buyer and seller. There is a process of proving validity of product for sale and buyer proof of funds. If you have more questions you can reach me at swhite@stic.net

Never heard of such a thing. The notes are typically assumed by whomever takes over the assets of the failed bank. If/when the resell those notes it won't happen immediately and it would typically go to a bulk buyer (like another institution) not a private investor.