Nobody pulled the plug. If you remember, when Christian is first urging Claire to let her mother go, he distinctly says that in Australian you can't just pull the plug because it's illegal. He does go on to say that he knows of a drug combination that will do the same thing, though.
Which means, if the funds ran out or something, the hospital wouldn't just pull the plug.
Also, yes, Claire's last trip to see her mom is when she's quite pregnant, and since she ends that scene by saying, "See you later," I assume it's because she's going to be leaving Australia on Flight 815 very soon, where she is just about as pregnant as she is in that scene.