Fischer is shot in the 3rd layer of the dream and enters the limbo.
In limbo, you are actually in your own mind, you don't follow the rules of others. What is more, you are so "sedated" (so deep in your subconscious) that you forget reality. This means, you don't have contact to anything else. You are numb (like in a coma). If you pay attention to what the limbo looks like, you'll see that being in the collapsing building (level 3) or in the water (level 1) doesn't seem to affect Cobb.
Probably that is why Fischer is fine. This is also the case of Saito. When Fischer is rescued, he gets very fast from limbo to dream level 1 (because of the sychronized kicks) and, as we remember, he was fine there. So you might say that at resurrection he "jumps over" two layers and returns to where he was just fine.
So what happened to Saito? Well, he and Cobb are in limbo and miss those synchronized kicks. The others get the kicks and wake up, destroying the levels 2 and 3. That means we have now only level 1 and limbo. So there are 2 possibilities:
Saito wakes from limbo directly to reality because they stay longer in limbo. He is not affected psychically because Cobb is there to remind him of the reality and to make him realize where he actually was (this was the danger: not to know what's real anymore).
They wake up in level 1 and manage to heal Saito (Fischer finds peace and has something to meditate, so his projections will not be a threat anymore). In the real world, Saito was shot in the stomach, giving him about 45 minutes before he died (so I have read). So after 15 minutes of driving, he still has 30 minutes, enough to create a hospital or an impossible structure to get fast to a doctor. I think he could be saved.
Now, you also asked why they didn't let Saito get into limbo from the beginning. Well, that was not a great plan, since going there is a great risk (you might forget who and where you are) so going after him would not be such a great idea, unless they had no other choice (which happens in the 3rd level).