If you use the "Open Containing Folder" icon for one of your downloads (usually on the right side), Windows should display the download highlighted in its current location. Hopefully then you can move it to where you want it to be. Does that work?

If "Open" and "Open Containing Folder" in the right-click context menu in the Download Manager window are grayed then that means that the file is no longer in the original download location and they may have been removed by Anti-virus or cleanup software.

It is possible that your anti-virus software is corrupting the downloaded files or otherwise interfering with downloading files by Firefox.
Try to disable the real-time (live) scanning of files in your anti-virus software temporarily to see if that makes downloading work.