Reference : Inception Explained
To talk of what happened, Mal shoots Fischer.
Mal is a Cobb's projection.
Cobb's mind is very affected by her death, he holds himself responsible for it. When his mind projects Mal, he projects her in a way that is out to ruin it for Cobb, that is his out-of-control guilt doing that.
Cobb, therefore, projects a Mal that attempts to kill Fischer. Her gun and the bullet that hits Fischer is also projected by Cobb. All the other people protecting the fortress is Fischer's projection.
Fischer experiences being shot in the 3rd level of the dream. The mind tends to believe what it thinks it sees and thinks it feels. Fischer starts to die. Once he dies he will wash up on the shores of Limbo. But that hasn't happened yet. Cobb and Ariadne think there is still one shot to get Fischer back. The way to do it by going down in to Cobb's mind at this point because, after all, Fischer is dying because of Cobb's mind. Fischer's dying mind can be reached using Cobb's mind.
They hook up the dying body of Fischer and Ariadne to Cobb's mind and go one level further down. Now, they do reach limbo, but this is because only 3 levels of dreams were architected. Neither did Cobb nor Ariadne die and reach Limbo. This is why they know where they are and what they are here to do. Also because they are in Cobb's mind, they know where they need to go because Cobb knows where Mal will be. Since the reason for Fischer's dying is Mal, if they find Mal, they will find Fischer and they do.
Now, they are merely in one further level of dream state below. To wake up, they need a kick in this level and one from above. Eames, from the level above, uses the defibrillator on Fischer and Ariadne pushes Fischer off the building giving him the kick in the current level (improvises). The synchronized kick brings Fischer one level up.
Fischer saw Mal shooting him and his mind accepted being shot. When he gets kicked back up, he doesn't remember the event that happened prior. Why? may be the shock of it all, waking up from a bad dream and just brushing it aside. They are all dreams at multiple levels after all. Fischer will suffer physical effects of being shot only if his mind makes that happen. In this case, his mind heads towards his dying father and focuses on that.
Saito, on the other hand, is shot by Fischer's militarized mind. Even if they went down into Fischer's mind, they would have no idea where to look for Saito because Saito was shot to protect his mind from getting attacked, Fischer has no obsession with anyone particular from his past. Besides, Fischer is being kidnapped, they would have to convince him to be the dreamer. Going down into Fischer's mind would also ruin the plan as they need to take Fischer through other dreamers deeper and deeper till the 3rd level and incept on his unsuspecting mind. The only thing they can do is hope to complete inception before Saito dies by descending further as the time dilation will give Saito more time to live. However, thanks to Mal being projected, they loose more time and Saito eventually dies and lands up on the shores of Limbo.