This first song is "Winter Was Warm," sung by Belle, Scrooge's former lover from the Ghost of Christmas Past. When I was a little kid and first saw the show, I absolutely loved it but this particular song was the least interesting to me. It was nice enough, but let's get on with the story. I am no longer a little kid, and understand and admire the great deeply-wistful charm of it.
The second song is "We’re Despicable," which comes from the Ghost of Christmas Yet to Come sequence. It's sung by thieves who have robbed the home of the late Ebenezer Scrooge. It really is the most unnecessary song in the show -- it doesn't advance the plot or develop character, it just reinforces the situation -- and arguably is the funniest and most fun.