q1) move should be fine, i've not personally had any issues with file names messing up with move compared to copy, although i'd suggest copy over move in case something goes wrong during the transfer then you still have the original data. you can install the dynamix file manager plugin to manage data from the unraid webui directly if you need that or install a container like krusader
q2) windows capitalization doesn't really matter as you can reference the data by lower or upper case no matter what the actual filenames are set as, with linux case matters so Media and media are 2 completely different folders. the way you deal with this is really how you want things personally and then just point things correctly
q3) you can/should use your current share and just point plex to the folders you are wanting the different libraries to be reading from.
overall i think you are doing it the correct way and the way that most would do it