I have only just signed up here on chess.com, so I'm not too familiar with the resources offered here on site, but outside of chess.com, I would recommend the endgame sections of www.chessvideos.tv:
Videos explaining certain mating strategies: http://www.chessvideos.tv/wiki/index.php/Videos_of_Endgame_Studies
Chess endgame simulation for practice fundamental checkmates:
http://www.chessvideos.tv/endgame-training/endgame-simulations.php
On my own blog, I have published some animated gifs of classic checkmate patterns:
http://thechunkyrook.wordpress.com/?s=mating+patterns
I think for the future, the chess.com crew may want to think about adding an endgame simulator like the one on chessvideos.tv. In my opinion, it's a very efficient and helpful tool to practise such rudimentary positions.
Would you please suggest me some good books on common checkmate patterns/strategies?
e.g. How to checkmate King with Queen and Bishop? How to do Legal's Mate? etc.