The drain leaks water as the drain in the sink is not sealed with plumber putty. The black plastic nut under the sink which tightens against the bottom part of the tub was glued in original installation and cannot be tightened or loosened.How do I break it loose to remove it so to replace with new drain? Does one have to hack saw it off above the nut and below the washer next to the sink or is there an easier way to get it off?

Cut the nut in a "pie-shape", then pull it off with some needle-nose pliers. It might be some work, but this will insure that you won't do damage to the sink.

XenoSapien