B: Do/Did you mean...? -I feel "Do you mean..." is the better choice when I try to think about what I would say... Example: "Do you mean she isn't getting married?" Did kinda makes it sound past tense to me... for example: "What you said earlier... did you mean she isn't getting married after all?" So I would use "do" if you're asking immediately after. Did if you are going back to something they said a little while ago. Or: What do/did you mean by ...? -This seems to me to be more asking them to elaborate/explain what they just said further. Again, do is better if it is the last thing they said. Did is better if its something they said a few sentences ago and you're referring back to it. Overall, which one you use "Do/Did you mean...? Or: What do/did you mean by ...?" really depends on the context and what you're trying to ask so I can't tell you without that. A: What I mean/meant is/was ....? -Again, I believe if you asked something he/she just said, they will say "What I mean is...," but if you're asking something they said in the past, they will say "What I meant was..." Hope this is correct/helps. Just from my ear and thinking about what I'd say.

You can use either without any substantial change in meaning.

That depends. If I am talking now and need to explain my words I use 'what I mean is that...'. When it is something that I said a while ago and someone asks me what I wanted to say at that time I use 'what i meant was...'