Is it possible to countersue prior to ejudication of copyright infringement suit? Will an attorney do this on a contngency basis?

You don't state what the "countersuit" would be for, but as a general matter, it is possible for the defendant in a copyright-infringement action to allege counterclaims, just as in any other civil litigation. It would be extremely rare for an attorney to take on such a case on a contingent-fee basis, because he is essentially representing a defendant and defense work has no pot of gold at the end of the rainbow.