Okay, maybe the wrong person to answer this, so someone correct me if I'm wrong. But I don't see why you couldn't schedule an ultra-sound whenever you want one, assuming the doctor and the equipment are available. As they showed, ultrasounds are often done in the doctor's office now, and are fairly common these days.
As for the pretending that she had a miscarriage, my thinking is that Terri believes that having a baby will keep Will with her and save her marriage. Having a miscarriage would keep that from happening, and more likely make Will angry with her, and possibly even blame her for losing the "baby".
Can't help you with the showtunes one. Didn't make sense to me either, but I went with it...(loved the fact that it was Kurt who said this...yes, the gay boy complaining about too many showtunes...)
"Are you calling me a procrastibator?" Hunter, [title of show]
"Guess who's gonna get blamed for the war in Europe?" Eugene, Brighton Beach Memoirs