”How did they get out of the “limbo” that the asian dude was in? If you could just kill yourself, why did they care about the asian dude dying in the first place? They should have let him die and then just have him kill himself to get out of it.”
That is basically what they did. The thing was, they were too heavily sedated for him to just wake up normally if he died. Drugged up like he was, he would drop into limbo, which is a shared and unconstructed dream space that he might not ever be able to return from. So the best option was to try to finish the job and get back before Saito died.
The trouble is that once you are in limbo, it’s easy to forget about reality; limbo becomes your reality. We assume that’s what happened to Saito when he went there—he wouldn’t think about killing himself because he wouldn’t realize there’s a reality to return to.
So, then! To summarize the kicks:
Level one: The van hits the water.
Level two: Arthur blows up the elevator.
Level three: Eames blows up the fortress.
Level four: Fischer and Ariadne go off the balcony.
All these kicks work, everyone wakes up on the first level, except Cobb and Saito, who are still in limbo. Cobb convinces Saito that this is limbo, not the real world. And then everyone wakes up on the plane in reality (or Cobb’s dream, depending on if you think the top fell or not).
The reason why, when Cobb and Ariadne follow Mal and Fischer into limbo, they end up in the world Cobb and Mal created is because of the entire group Cobb was the only one who had been there before. What they saw was everything that was left from that experience. Presumably, if someone else in the group had also been there, it might’ve been something different.
FYI: It took two people to write this answer, and we’ve seen the movie a collective five times. We could be wrong… but probably not.