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The package manager warning may be because Fedora is checking for updates on its own, in the background, while you are trying to install Parallels Tools. I think it defaults to waiting a few minutes after you log in to do the update check. So maybe try waiting a good while after logging in before starting the Parallels Tools install.
On mouse issues, until you get Parallels Tools successfully installed, your Fedora isn't using the mouse driver that would work best. So you really need to get the PT part done before trying to troubleshoot mouse, file system and video problems because PT installs drivers or kernel modules for all of these.
Just an aside here too -- Fedora gives you a few choices in desktop managers - Gnome, KDE, etc. I have had good luck using KDE and not such good luck using Gnome. I think they use different windows compositors, and one works ok with the Parallels video driver and the other does not.