Do you mean:
--------
When we ask a question about "meaning" (on forums), the present tense would be an appropriate question and answer. For example, "Do you mean ...?""Yes, I do."(rather than "Did you mean ...?""Yes, I did.") , because the text of the original poster is visible to us, so we see it as being present now.
Well, that's not exactly what I meant, but it may be a reason, depending on the context.
Case 1
Tom: Hey, you!
Bob: I'm sorry. Do/Did you mean me?
Both are possible. I'll explain why below.
Related side point:The sense of mean here is similar to 'refer to'. Bob could say Are/Were you referring to me?
Case 2
Tom: Perhaps we should try another approach.
Bob: What do/did you mean?
In these two cases I think "do you mean" is appropriate because Bob replies to Tom immediately. Even though technically the time has gone past, we can ignore that.
Yes. Only do is appropriate here. Both Tom and Bob are presently engaged in the conversation. Compare this to Case 1, where the two speakers are not presently engaged in a conversation until Bob responds. I do think though that the present tense Do is more likely in Case 1 because, from the moment of Bob's response, they begin to be presently engaged.
Related side point: Can you see how the sense of mean is different from in Case 1? It does not mean 'refer to'. (Well, what Bob means is not obvious from this. In fact, he could mean What are you referring to? but I imagine a paraphrase of Bob's response as: Please expand on what you just said.)
Case 3
What did he mean by that remark?
I am not sure in what context we can use the past tense in the sentence. Maybe a longer interval between his mark and the speaker's saying this sentence? For example, he gave his mark one hour ago, yesterday, last week, etc.
The focus (the remark) is clearly an event in the distant past. It does not matter whether it was ten seconds or ten years ago. The idea is that the speaker is thinking about the remark as being in the past. Contrast this with Case 2.
Case 4
What was meant by the poet?
Is this case the same as Case 3?
Yes. But it seems to me like an odd, and quite unnatural example. I think that the present tense would be just as likely, if not more likely, because as you have noticed, when we read written texts, we tend to use the present tense to talk about them. This is because we are presently engaged with them. We even use the present tense to talk about writers who have been dead for hundreds of years. (E.g.
Shakespeare is saying in the play that ... Confucius says we should ... Lao Tze thinks that ...)
I've noticed that many of your questions relate in some way to the idea of present time. I'd like to remind you that the notion of what we call 'the present' in English is really quite undefined. It does not simply relate to an instant in linear time. It very often describes a fundamental kind of psychological experience (I like to call it a 'mindframe') that can extend indefinitely into the past/future. In Case 2, essentially, it really does not matter how much time has passed between Tom and Bob's utterances. Imagine that instead of a spoken conversation it was a conversation by email. They would still likely use the present tense to refer to each other's comments, even if they only emailed each other once a year. The point is that they are presently engaged in discourse. The fact that their emails are written is not crucial to that, though it does make it very obvious. It is still possible to say what Socrates
thinks even though he never wrote anything down, as long as we feel that his thoughts are present to us.