Your question in its current form starts off with:
Is there any library for .NET for recursive Copy and Move file operations that performs in a manner that would lead to as minimal partially completed results as possible?
And there's your problem. You're asking for a library recommendation based on the criteria you list after that. Such questions are regarded to be off-topic for Stack Overflow on the basis that they are not-constructive. We don't do recommendations. They tend to attract poor quality answers.
This has the potential to turn into a list of different libraries recommended by users, one possibly not any more correct than the other. Which is not the kind of answers we want to have. They are of the open-ended form as hinted at in the FAQ.
So in its current form, I would not have voted to reopen it, even though this seems to have happened by now. I would however not be surprised if it gets closed again.
Often questions like these however can be turned around by a rephrasing of your question. Instead of asking "Is there a library that does X?", with you intending to solve a problem, you can ask "How do I solve this particular problem?", the answer to which might well be "Library X will actually do that for you". These are subtle things, but the latter question might be more likely to invite good answers than the former.