Yes, it’s possible. I don’t remember right now how you do it with the installer, but at least you should be able to copy the whole (first) installation to another location. Then the new one doesn’t find it.
(EDIT: you probably want to install 5.1 first, then move it, then install the nightlies to the default location. That way the new nightlies will overwrite the older ones but don’t interfere with 5.1.)
See the document linked above. You need to set only KICAD_CONFIG_HOME before starting; the rest you should set inside KiCad when it’s running. Be sure not to install environment variables with the installer, and if you have something set already in your Windows, delete them from Windows.
Yes. What are you doing for the Kicad system path variables? Because I believe that those for v5 will not be good for v6. Last but not least where can I download nightly builds for v5 and v6? I found the nightly builds directory:
One more word of caution : Data files (pcb, schematics etc.) opened with v6 can’t normally be read back in v5. There are file format differences. So pay attention and make backups if you risk something.
Again, the document linked above explains it, although I understand it’s long and verbose and may be difficult to digest at first reading. The point is that you set only KICAD_CONFIG_HOME before starting each version. When you run each version for the first time, open immediately the Preferences->Configure Paths dialog and set the rest of the needed variables there. They are saved to the config file of each version.