Good question. "I must be going" is sort of idiomatic. It does mean "I need to leave." But in general, "I must be [X]" means that you are not sure that this is true, but you think it is probably true. "He always gets good grades. He must be really smart." (meaning: I don't *know* that he is smart, but I know that he gets good grades, and therefore I believe that he is probably smart) "It's time for the meeting, but there's nobody here. I must be in the wrong room." (meaning: I'm not sure that this is the wrong room, but since it is empty, I think it is probably the wrong room) If you say "I must be studying now," it sounds like you are not sure whether your are studying or not, but you think you probably are. This doesn't really make any sense. Instead, you can say either "I should be studying right now" or "I need to be studying right now." (The second sentence sounds a little more urgent.)

No, 'I must be studying right now' isn't natural. People would think you were trying to say, "I *think* I am studying now" which doesn't really make much sense. I don't think it's what you meant, either. If by 'must' you meant 'obligated' or 'have to', then you should say, "I must study right now".