Someone, perhaps Michael Caine has discovered a way to enter, and control yourself in dreams. Certain people, are capable of building the dreams (architects)
This has become to some degree common knowlege amongst the public or at least important people. Theres a company who specialises in it (employing Cobb in the beginning) and the the people who train Robert to protect himself.
Fischer is about to inherit his father's energy company which is about to gain a monopoly over the industry. For this reason Saito, who runs a competing conglomorate hires the best team he can to try an inception to save his company.
An idea has to be planted deep to convince the subject it is there own.
The actual real world is on the plane flight. They are sedated for 10 hours.
The first layer of the dream is the city, Yusuf stays here to protect the team fromt he unexpected security but mainly because he needs to kick the others back from the second layer. Once there back in the first there isn't a kick, they simply have to stay and wait for the sedation to end and wake up regularly.
The second layer is the hotel, Arthur stays behind here, again to protect and kick back from layer three.
Three is the "safe" level. They have no intention of going further then this.
Most people as Cobb explains hide there secrets in a safe. Because Fisher is trained to protect himself, his layer is instead a fortress in an artic wasteland with a secure vault. His secret is his father and what he wants for him.
The inception is convinving Jr. that his dad wasn't dissapointed in him, but rather his choice to follow his footsteps. Knowing that Rob will be motivated by his dream to change his life and in the process disband his monopoly over the energy industry so he can do what he wants to.
Cobb as usual can't control Mal and she kills Fischer. He doesn't wake up due to the sedation so he goes into Limbo. The only Limbo available for him at the time, is Cobbs because thats who he knows in the dream at that point. He doesn't know Saito and doesn't understand whats happening to create his own limbo, so he by default is stuck in Mal and Cobbs world.
Thats why they go into kick him once again and bring him back up to 3.
Cobb on the other hand begins to realise he can't control Mal anymore and is starting to be unable to distinguish reality from dreams. He, with help from Ariadne incepts himself to believe Mal is truely dead.
Therefore the world they built togeather for all those years ceases to be. That is why he washes up on Saito's shore of his own Limbo, its now the only person Cobb knows there.
Cobb was an architect, not something everyone can do. Upon realising hes still in Limbo and seeing Saito, he knows that he can build a new perfect dream world with his friends, and his kids.
If he did actually wake up and go back, he would be screwed. Saito was the one with the connection to get Cobb back into the U.S. without being arrested. Saito is still in Limbo however. He cannot help him and Cobb realises this will be the only way to see his children again.
Therefore Cobb creates his dreamworld from what he knows, the memory of his kids in the backyard, the memory of all his friends seeing him off, of Michael Caine in the exact same outfit coming to pick him up. He can, like Mal did, forget and at least find happyness with his children, there he can grow old togeather with them. Even if he's in a coma in the real world and only lives a week, thats a lifetime for him to spend there being happy. Him walking through the airport and trying to get past security could be him convincing his own mind hes not dreaming and to let him past.
As to the very end with the Totum, it does appear to faulter, however I believe this Ariadne(also an architect) planting an inception in his own mind to help put his mind at ease and help him forget its just a dream, so he can just have what he wanted, time with his kids again. Its the way she says "hes gonna be fine."
As Arthur explains your totum can be manipulated, he knows the weight of his dice. However to manipulate Cobb's all one would have to do is know it spins and stops, not its weight or feel. Escpecially because Cobb shares the way he got his totum from Mal and its importance to him.