Gustavo chooses Kendall to go to Los Angeles with him because he describes him as having the fire. What is this fire exactly? It is the one Kendall displays throughout the entire show, the ability and willingness to talk back at people for something he feels is wrong, as well as the resourcefulness to come up with all his "Kendall plans". Gustavo practically chose Kendall because he(perhaps subconsciously)knew he needed someone to challenge his authority when necessary, and his stunt at the auditions to defend James proved he had the guts to.
Why was Kendall the only one of the band not to suffer from "Hollywood Fever"? Because his family moved to L.A. with him.
Why was Wayne Wayne so determined that Kendall would be kicked out of the band in Big Time Bad Boy? Because he was already the group's bad boy - Notice that when the guys are told that one of them has to be the bad boy, Kendall was the only one not willing to take the role. He's the bad boy, but not in same way the cartoonish Wayne Wayne was.
When the battle lines were drawn in "Big Time Pranks," James asserted that they were short one, since there were ten girls and only nine boys present in the hallway. But in fact, there was a tenth boy in the prank war - Logan, who was believed at the time to still be in their apartment. Logan was actually in the hospital after inadvertently pranking himself out of the competition, but they didn't know that yet. When Jett joined the boys, supposedly making it an even ten against ten, it should have been viewed as eleven boys against ten girls.