Here's the order I could reconstruct (please feel free to edit with changes if I got anything wrong):
Ragnar, Francisco, and possibly Hugh
Midas Mulligan and Judge Narragansett (both related to Judge Narragansett's ruling in the Lee Hunsacker lawsuit being overturned)
William Hastings quit about a year John Galt. (He worked for a ...
I just did a quick scan of the book (online PDF) and I'm of the opinion that it's impossible to know for certain. I think we can know the sequence of the first and the last, but not most in the middle, because that information is never stated in the book.
Ragnar, Francisco (maybe Hugh?)
The Last (in reverse order):
I don't think the book ever answers what the question was, so I'd like to take a shot at your more subjective question:
what might it have been?
There's a question that is asked a number of times throughout the book by the heroes:
"By what right?"
A few examples:
What motive moved them?—what was their knowledge?—which one of them,
unaided, could ...