I'm running out of space on the partition that has Visual Studio installed. It's safe to copy the installation in another partition?
Without having tried I bet this isn't possible.
Installation folders are typically stored in many places such as config files and the registry. After moving, all these references will still point to the old and now invalid location. And, even worse, moving the folder will also break any installation / uninstallation / update routines which means that you will no longer be able to install patches and service packs.
Conclusion: You are way better off uninstalling Visual Studio and moving it to the new location. It takes only a short time as compared to the headache that you would end up otherwise.
(Or, if you don't like to do that you can of course still mount a new partition to the program files folder to increase disc space or get a larger hard drive)
No, that wouldn't work with any newer versions of Visual Studio. If it's pre-2003 you might have a chance.