Question about The Big Short

In the movie The Big Short, Michael Burry buys CDS against the housing market, betting against a market which historically has done very well. Okay, fine. But 1. The movie acts like Michael Burry invented the CDS, which... No he didn't, and 2. Because he was the first to do so he has to pay very high premiums. If Burry is betting against AAA MBS, shouldn't his premiums be low, not high? Also, the movie acts like for Burry to be right, the defaults have to occur. But being long CDS generates prof