WMG / Birds of Prey

The reason for Batman's absence in the series is...

He ended in a dimension that happened to be the Revolution. It took him quite some time to find the means to escape and get back into his own dimension. Evidently, his call to Alfred at the end of the show demonstrates his success in returning.

In 2051, Lady Shiva will get her promised duel to the death.

In issue #6 of the relaunched series, published in January 2011, a death duel between Huntress and Lady Shiva gets cancelled by Black Canary. Shiva, having given her word to take part in such a fight, wants to continue, but Canary reminds her that she did not agree when such a fight would take place, and that it could be "forty years from now." Maybe it'll still be against Huntress, or even Black Canary herself as originally intended.

TV series
If the series continued, Dinah Redmond would have eventually taken the Black Canary name.