What does would've mean here?

GPY

anonymousPast of will be is "would be" and past of will have is "would have"? Am I correct?

In regular cases, yes, but your sentence is more complicated.

anonymousSo, in this sentence "would've" has been used so the retrospective past-tense version could be like "It's unlikely that President Putin will have likely responded to the ultimatum(by midnight in this context)." Am I correct, Sir?

In this case, no, I think not. I think the past sentiment was "It's unlikely that President Putin will be likely to respond to the ultimatum" (horrible sentence but trying to preserve the original), as I mentioned. In the context of your sentence, "would have been" fits the sense of "we thought in the past that he wouldn't respond (in the then future) and we know now that, indeed, he didn't". To a certain extent "would have been" is triggered by "It's unlikely, ...", I think.

This is my interpretation, but ideas about how to explain "would have been" in this sentence are very likely to vary between different people.

One last follow up question, Sir. In this context does "respond to ultimatum" mean to explain about the nerve agent by the midnight last night from Russian side.(according to the video)?