1. a) If I understand your question correctly, you are referring to some prior art authored by a third party. This is typically raised in defense to infringement claims, and the party seeking to invalidate a patent has a very heavy burden of proving that this prior art indeed renders the patented invention invalid (not novel or obvious). This is particularly difficult when the prior art reference was before the examiner during prosecution of the patent.
b) I believe you refer to some prior art that was in the accused possession, but was never publicly disclosed at the time of filing of your patent application. If never publicly disclosed (the legal test and analysis will depend on many factors), it would not be considered prior art to your invention, but could possibly be used as part of the "obviousness" challenge (showing that others contemporaneously came up with the same solution to the problem, and therefore such solution would have been obvious).
2. If you sue C for infringement of your patent A, which is an improvement on patent B (owned by another party - X), C has no standing to challenge you for infringement of patent B. Also, in order to be accused of infringement, you must be producing, using or importing some product or method. You can't infringe anyone's patent by simply asserting an improvement patent that you own. Do you produce, use or license any products or methods that are covered by your improvement patent A? If so, you would need to talk to an attorney about potential claims from B, which are independent of your lawsuit against C.
-Daniel
Solton Rosen & Balakhovsky LLP
www.srblaw.net