Slumdog Millionaire questions (1, 2, 3)

What does the title mean? How does the title and the contrasts within it provide symbolic summary of the film?
The title is a little paradoxical because a slumdog is like a person who lives in a poor place and lives the "low life" and a millionaire is, well, someone who is rich and wealthy.
It's like a small summary of the film because Jamal was always considered a slumdog, but then entered "Who Wants to be a Millionaire?" and became a millionaire himself

Early in the film we see the young Jamal dive into a latrine pit to steal a glimpse at a visiting movie star. How does his single-mindedness to see this movie star reveal his determination? What other examples do you see in the film of his
determination?
Jamal wanted to get the autograph no matter what, he was determined to get it even if it meant diving into a pit full of waste.
Another example would be when he wanted to get back with Latika. He went to the mansion where she lived and lied to get in. He assured the 'receptionist' guy or whatever that he was the dishwasher they had asked for. He dared enter the domains of a gangster just to see Latika again, with lies and everything but he got it. That's what I call determination.

In the film, the theme of destiny is a central theme. What does it mean that all Jamal desires is just out of his reach? (The prized autograph, Latika, his brother, the answers, etc.)
Apparently, Jamal had a very bad luck; he got the super autograph but Salim sold it, he met Latika but they got separated, his brother Salim was affected by greed and all and he kicked Jamal out, the answers? He knew most of them because he lived them.
However, it was Jamal's destiny to get Latika back and to know the answers, as tough as it was. As it was said in the movie he'll win because "it is written"