Those kids grow up to be Batman-style superheroes.The kids who were home-invaded are pretty much average ordinary people. Though their parents are dead, they never forget the hero that saved them from the same fate. They would want to be just like him one day. They would be to David Dunn what Batman would be to Superman.
Joseph will get superpowers.Because he only has half of David's genes, he would get some powers but not all of them.
David has Superspeed.One of the things that was talked about alot in the film, was David's reputation as a former football player. To be a great football player, you'd need strength, speed and endurance. Since David was considered a star player and has been proven to have strength and invulnerability. Maybe he's a fast runner too thanks to his strength.
David was abducted by aliens like those in Signs.Their experimentation gave him his powers, which is why he reacts badly to water.
Elijah Price can see the future in some way.At the end of the movie, it's revealed that Elijah has been causing accidents to find someone invincible, someone that would be his opposite - a hero. Elijah tells David that he is David's archenemy - in a way - and that they should have know because he is David's opposite. Okay. Now, if David is invincible, super strong and can see people's pasts, then it makes sense that Elijah is weak, has brittle bones, and can see the future. That may even be part of why Elijah was trying so hard to find a hero - he knew that there was a person that was destined to do these great heroic things and change the world, but he had to cause it in the first place. On the other side, he might have known a great evil was coming, and that a hero would need to fight it.