Never used OS/2, so maybe you can clarify this for me:
I thought that one of the limitations of OS/2 was that while it could run DOS programs, it could only run one DOS program at a time (in addition to a number of native ones). Is that correct?
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.
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.
I thought that one of the limitations of OS/2 was that while it could run DOS programs, it could only run one DOS program at a time (in addition to a number of native ones). Is that correct?