So I have a bug fix (green) and owner also made a bug fix (red) but I would like to rework both of them due to discussion we had. I have opened a PR and there is merge conflict that can't be resolved. Should I open a new branch in my fork and close PR or should I google some rebase magic to apply commits to my bug-fix branch.
It depends - as with any real answer to a problem. I would likely start with a rebase of you bug-fix on 2.0, resolve any conflicts that might have. If there are multiple commits on bug-fix I might squash them to make the merge easier. But if the conflicts are too complex to really resolve it might be easier and quicker to just redo the work in a new branch if the changes are not that big.
Which was is better for you depends on how big those merge conflicts are. But it seems like a good opportunity to learn how to rebase and how to resolve merge conflicts.