As I see it, the movies that Bollywood copies that turn out to be popular or good, they're just taking American movies, and making a couple of adjustments to the plot and making it for more Indian audience.
And why MUST there be dancing and singing in ever Bollywood production? Maybe I did not see enough Bolly movies to judge about that?
The majority of Bollywood movies have singing and dancing. The only 2 movies that I remember that don't have singing and dancing in is Chak De India and Gandhi my Father.
Also, one reason why so many movies have singing and dancing is because, besides that everybody likes singing and dancing, and it Bollywood's trademark thing, is that life in India can be pretty hard compared to many places like America or Canada. People don't want to remind themselves of that when they go see a movie, they want to have some fun during the movie. Sure, they might make a couple of serious movies that become really popular, but usually they like to enjoy a movie and take their mind of how hard life is. Atleast that's my theory.