Yes, you can have multiple versions of Inkscape installed at the same time. While it's typically not thought of as a safe practice (with computers in general), it it possible with Inkscape, without worry.
You just have to be sure not to install them into the same directory. Make a new folder for each version.
As long as you either use Inkscape's AutoSave feature, or otherwise have some form of backups, you shouldn't have to worry about losing work.
As far as I know, all Inkscape files are backwards compatible. You can open any file made with Inkscape, with any version of Inkscape. (Although if you went back far enough, you might find features that can't be supported.) But you can open a file which you created with one version (older or newer) in another version (older or newer), without any problems.
Clipboard or cut/copy/paste..... I guess I can't answer that. I use Duplicate almost exclusively. The only time I might use Cut or Copy is if I want to take an object from one file, and paste it into another file. I guess Inkscape would not care which version you were using when you cut or copied something. But again, I don't have any notable experience about that.
I guess I must have....5 or 6 versions myself. Although I do avoid having more than one version that's technically installed. The reason I avoid having more than one EXE or MSI, is because Inkscape could get confused when I'm ready to uninstall them. All the other versions I have downloaded the 7z package, and they all have their own folder in Program Files (or Program Files (x86) as the case may be).