1) They hooked themselves up to the machine again in the dream to go down another level. In order to get out, they need to be simultaneously "kicked" in all the levels.
2) They do this because their reasoning is that pure inspiration is much harder to do that just extraction. For it to take and for the subject to believe it's his own idea, they need to plant it deep enough into his subconscious.
3) Heretic would disagree with you

, but there are moments in the film that state/suggest in dialogue whose dream they are in, although they all share the experience together and can project certain things if they can't control it. This is why Mal and Cobb's kids show up all the time no matter whose dream they are in. The dreamer holds the dream together and can change the environment, while the subject is the one who fills it with people.