VMS and CHD are not in my Vocabulary

If there are multiple .cdi image files for one game, it's very likely a multi-disc game. Do what you'd do with a real game; open the load the first disc in Demul (use the gdrImage plugin that should have come with the emulator), and play. When the game tells you to load disc 2, there should be an option to switch discs without stopping emulation.

You'll manage VMS files via the VMS Manager. Just create a new file and name it, then format it, and select it as active for Port A. The interface for it is a no-brainer, so it shouldn't take you long to understand it.

No need. Resorting to YouTube in a problem like this is an utter waste of your time. And mine. Concise desciptions are key, and if you don't understand the jargon involved, use substitutes. We can work out the kinks as necessary. Screenshots work wonders too, but if you need more than three to get your point across, you're doing it wrong.

Anyway, what you have is a RAR archive that's split into three parts, with one single disc image within, not three different disc images in three separate archives. Open the first part with WinRAR or whatever archiver you use, and extract the disc image to a folder of your choice. The other parts follow suit automatically.

Let me put it this way: once you've extracted the content from the first archive (game.part1.rar), you are done. There is no need to extract anything from the other archives (game.part2.rar and beyond); they've already be processed.

Now, if your situation is such that you actually have a game that really has more than one disc, and the filenames of both disc images happen to be same (highly unlikely, but hell if I know) - simply rename the first disc image to something else, then extract the second disc.

If it wasn't clear the first time around: The RAR archive format in its current form and specification always tags an archive that has been split into multiple parts by appending .part1, .part2, etc. to the filenames. RAR automatically combines the split contents of the individual parts during extraction.