make sure that your displayed nurbs model is at its highest detail setting (press 3 on the keyboard). It's possible that the snap to curve function is referencing the "actual" curve rather than the lower detail displayed curve.
It should be noted that trimming a nurbs surface is not the same as detaching. You are, in essence, creating a type of transparancy of the surface that makes it appear as if the trimmed area is no longer there, but if you were to go into, say, edit CV mode, you'd see the surface's completed CVs in place.
It's been so long since I've used nurbs I'm afraid I can't answer the 2nd question, but good luck.