The speculation about the DDM being a vengeance weapon makes the least sense of all. No vengeance weapon would operate in such a haphazard manner unless badly broken - and if the DDM is badly broken, there's no prerequisite for it to have been a vengeance weapon to begin with.
A berserker would make more sense. If the creators believed that planets give birth to enemies, destroying all planets would be a good idea (although concentrating on already inhabited or inhabitable ones might be more efficient, if the creators knew what standards of inhabitable the enemy would follow). But the DDM does
not destroy all planets - in the L-374 system, it left the job half-done. Right after digesting 400 people, interestingly enough.
But as long as we accept "broken", the DDM could be a terraforming machine, too. Or simply a mining tool that has gotten confused about its target parameters.
The thing is, our heroes can't tell. Their speculation about vengeance weapons is utterly baseless; the theory about an extragalactic origin, doubly so. There's no telling what the machine really would do when reaching the Rigel colony/ Rigel colonies. If greater starship resources were better spent in trying to understand and perhaps control the thing, a "dumb beast" could easily be manipulated into being harmless or even beneficial; a "sapient tool", even more so.
To make this at least tangentially relevant to the subject matter, we have to wonder why Decker was a Commodore (apart from the dramatic necessity of making him unambiguously Kirk's superior). Did he command a fleet of vessels, like Commodore Wesley arguably did in "The Ultimate Computer"? The subspace jamming effect of the DDM would cut Decker off his other assets efficiently enough.
Kirk was commander of the Flag ship
Where? When? We never learned that either the TOS ship or the E-A would have enjoyed flagship status (except perhaps briefly in "The Menagerie" where Commodore Mendez flew his flag aboard the ship; all the other flag officers were mere passengers aboard Kirk's command).
Fleet Captain, however...
...Could simply be the longer expression for Captain. To tell Jim Kirk apart from Leo Walsh, that is: some captains are (Star)fleet captains, others are not.
The only time the concept of "fleet captain" is mentioned is in relation to Christopher Pike. Perhaps he already held the credentials of captain from some civilian context, so his promotion to the Starfleet rank required special clarification?
Timo Saloniemi