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On an 80286, OS/2 could only run a single instance of DOS due to that processor's lack of a true virtual 8086 mode.

No, OS/2 2.0 and later could run any number of DOS and Windows 3.1 applications at once. I'm not sure about the 1.x series. You're probably remembering Windows 9x's feature of being able to automatically reboot into MS-DOS for running games.

You are correct.

I don't think that's correct but can't remember well enough to say so definitively. You could certainly have multiple DOS and Windows programs "running" but whether they were all active simultaneously or not I can't remember.