It is well known that "When are you graduating?" or even "How is your research going?" can be touchy questions among graduate students. But this is well known in part because they get asked these questions constantly, including by each other. And even if they can be unpleasant to answer, they are still fair questions. I'm not sure that the problem lies where you think it does.
I'm working solely on my dissertation project now, and I'm working as quickly as I can.
That's a pretty defensive thing to say straight out of the gate. Basically you sound like you want to ward off in advance any thought of optimizing or improving your path to the PhD. An academic who sees no room for improvement is setting the bar pretty low. I am a tenured faculty member, and if you came to me saying, "I think you could work faster / more efficiently / with greater output if..." then believe me, you would have my attention.
We have group meetings once in a while. Another faculty member and his student also attends because they collaborate with my advisor. In the past several meetings, my advisor has been too busy to attend.
Forgive my prying, but I have already seen something that to me looks more serious than some other faculty member asking you some questions you don't like. Your advisor is too busy to attend your group meetings? You know, I think you might work more quickly if....
When I say "no" "I don't know" etc., he has an expression of concern (or maybe pity).
Both concern and pity are positive emotions. This guy sounds like he is -- you got it -- concerned about you. The fact that he is showing up at several consecutive meetings while your advisor is not makes me think that he is indicating a desire to help you out.
I am really annoyed by this. It's like someone keeps on asking me about my fish when it died recently.
I find your simile to be pretty strange, but I'll try to play along: isn't it like he's asking about your living fish who has looked a bit less than healthy recently? Maybe I'm not getting the picture: who or what has died in your recent life, metaphorically speaking?
I'm already under enough stress trying to do research.
Yes, you sound like you are very stressed out. People who are too stressed out are not doing things in the best possible way, or even in a healthy way. Most commonly there is some kind of disconnect between their future hopes and their present actions. Talking through that kind of dissonance, and adjusting either or both, could be very helpful.
The last thing I need is someone reminding me I'm behind schedule - it's demotivating.
If being reminded that you're behind schedule is demotivating, then something seems off-kilter. Being reminded that you're behind schedule should be motivating, unless the schedule is not reasonable, in which case that should be directly addressed with your advisor. If it has been, then the problem seems to be that you haven't been honest enough about your situation. If he expects you to graduate next semester because you're an Nth year student, and you and your advisor have decided that you're not going to graduate until the following semester, just say so.
Not to mention this makes me look bad in front of my group mates.
Your group mates should know your situation better than someone who has been sitting in for a few weeks, so I don't really understand why this makes you look bad. Unless they don't understand your situation and these questions are revealing it....which is not the visiting professor's fault.
What should I do? Tell him bluntly "it's none of his business"? Stop attending group meetings?
Stop attending group meetings?!? Presumably the group meetings are an important part of your own research and progress [although with your advisor absent, I have to wonder...], in which case not going would be a terrible overreaction. (If they are really not valuable, then okay, don't go. You'll work more quickly without having that waste of time. But tell your advisor about it: why is he having you go to meetings that are a waste of your time?)
I think the bottom line is that this faculty member is trying to be helpful, but if you have fallen into an interaction with him that from your perspective is only getting you down, then you should talk to him directly about that. I would suggest making an appointment with him privately and at that appointment have the conversation that he wants to have all at once. Tell him about your situation. You can tell him that you think he might be concerned about you but that now that he knows Extra Information X, you hope that he can see that you are now firmly on track. If he disagrees, then he can share his opinion with you privately and perhaps even give you some actual help. At any rate, one can only ask questions like "Have you formed your committee yet?" "How many years have you been here?" so many times. If you give him the chance to spend as much time as he wants asking those questions, then with any luck he won't ask them again at your group meetings, and if he does you can say, justly, "We discussed this thoroughly last week, so I don't want to take up everyone else's time revisiting it now. We can talk later if you like."
Anyway, please don't dismiss the idea that this faculty member could help you out. Good luck.