Group minds are a science fiction concept that come in several forms, which you may read about at this article mythcreants (click link here). As the article explains, there are essentially three types of group mind relevant to this discussion: "hive mind" (every member shares the same mind), "overmind" (the species is ruled by a dedicated leader caste, provides a handy weak point too), and "egalimind" (members may share all thoughts, but retain their individuality).

The zerg's group mind has behaved like all three of these at different points in time.

In the zerg history in the SC1 manual, the Overmind (the character) was a true hive mind (the article definition) composed of the amalgamated minds of the zerg race. In the Precursor/Loomings campaign, we actually see in this action because the zerg inside the installation are able to coordinate and even display enough intelligence to hijack the security system despite being composed only of minion breeds without any leadership breeds in sight. Whenever feral zerg are encountered in the games, they are able to coordinate and expand hive clusters just fine despite their shtick being that they lack leaders and are a danger to themselves and to everything around them; this cannot simply be explained away by "gameplay trumps story" because the author could easily have avoided the logical contradiction by claiming these zerg went rogue rather than feral (as in the Insurrection campaign).

The manual initially introduces the zerg as a true hive mind, but then complicates matters by somehow laying an overmind (the article definition) over top of this. The explanation for this is that the leadership caste were created to boost efficiency: the Overmind delegates tasks to them to perform on its behalf. Apparently, since it is not clearly explained in the text, the Overmind is not able to multitask like hive minds are explained to do in the article. In order to divide its attention, it seemingly needs to partition its consciousness. In Liberty's Crusade, author Jeff Grubb tries to explain this inconsistency by claiming the zerg "operate off a hierarchy of hive minds, each greater than the ones below it, growing up to near-planetary consciousnesses" (pg 160). Judging by the context that here a hive mind is equivalent to a contiguous consciousness, I think he used "hive mind" in the same sense as the article.

The cerebrates (and their substitutes like brood moms and pack leaders, who I will all lump under the cerebrate label because there is no functional difference) are the only zerg given much in the way of characterization. The secondary agents like queens, overlords and infestors have all been either stated to have at least human-level intelligence or been seen in the fiction making monologues or speaking with others. The cerebrates constitute an overmind as described by the article, but their connection to each other (at least prior to brood war) seems to be more akin to an egalimind. They cannot conceive of deception or treachery, but according to the SC1 manual their relationships can be fairly dysfunctional (e.g. Garm/Zasz is considered whiny and unstable, Surtur/Kagg is so bloodthirsty that it causes collateral damage to other broods, Fenris/Nargil sometimes has to hunt down "escaped breeders"... whatever that means in this context).

The zerg's group mind seems to behave according to whatever was convenient for the writers at the time, rather than what was consistent. This can be seen in the fact that feral zerg had to be exterminated in SC1, but in BW they are easily reclaimed. When they need to be enslaved or easily defeated, they operate according to the little-o overmind model: drugging a cerebrate lets you control its broods, killing it means its brood is mindless and will default to the control of the nearest other cerebrate, etc. When you need some random feral zerg to fight or win against the protoss forces defending Aiur to justify cheap conflict, they operate like a true hive mind.

If the zerg group mind operates according to writer convenience, there is no way to build a coherent explanation for it because that requires the writers to follow consistent rules which they emphatically do not. There are numerous idiosyncrasies, ramifications and inconsistencies.

The fact that broods may be turned against other broods by drugging their cerebrate, and that they may exchange control of minions, suggests any number of things about the structure of their communications. It means that broods have some kind of authentication system that distinguishes their minions from one another so that minions of one brood do not follow the commands of another brood's cerebrate. This, of course, contradicts the ease in which feral minions are seen to be reclaimed in canon so I have no way to explain that without positing that zerg are capable of forging authentication signatures (which opens up a whole can of worms regarding psychic warfare). The hive mind emulator in WoL suggests this is the case because it claims to spoof the Overmind signal which all zerg below a certain intelligence threshold will automatically obey over other signals; this plot has a major hole in that you would think the zerg could trivially plug this weakness by reprogramming their minions not to respond to it, because in real life we do the same for computers every time we patch vulnerabilities. (Of course, this is far from the first time that the starcraft lore has ignored the entire concept of arms races and critical thought.)

The fact that the zerg seemingly need to be in proximity to one another to facilitate communication suggests that their telepathy has limited range (like, you know, all forms of communication in real life and all the exotic systems seen in the lore like telepathy). Cerebrates are able to communicate with other cerebrates and the Overmind over arbitrarily vast distances. Cerebrates are only able to communicate with their own brood over roughly planetary scale. Overlords, queens, and infestors need to be on the same field as their minions. Minions coordinating on their own need to be in the same installation or space station.

It is never spelled out (like so many other things), but protoss and zerg telepathy seem to operate on difference psychic frequencies if a khaydarin crystal is not being used as a reference point (which itself suggests the xel'naga used a third frequency). In the SC1 manual Tassadar read a deep space probe's mind by linking it with a crystal. The psi disruptor and devices based on its principles do not affect protoss communications. EMP weapons designed to jam protoss communications have no effect on zerg. In SC1 episode 2, the zerg are incapable of detecting the protoss forces landing on Char even though their shtick as a species is that they are sensitive to psychic waves (although to be fair these were dark templar so they probably developed psychic cloaking simply to hide from the protoss empire and adapted this to the zerg). As we see in the Revelations short story, and implied by episode 2, the protoss are capable of intercepting zerg communications enough to learn of the Overmind; although it is not explained if this requires khaydarin crystals to serve as a translator (though I would assume so since it was explained in their first contact). According to the LotV field manual, the protoss learned how to hack terran technology and use it to transmit their own communications (which is no surprise considering this would probably be common practice under the great stewardship).

I had a few ideas for explaining the zerg group mind, but again it requires following a consistent logic so it is only of value to my fanfiction.

If the zerg operate according to a true hive mind, it should never be possible for them to go feral because they automatically link up with all zerg in proximity and their intelligence scales with the number of zerg in the hive mind. This is why the ostensibly feral zerglings and hydralisks in the Precursor/Loomings campaign were able to understand and exploit the technology in the Confederate installation. Adding an overmind model on top of that does not make much sense unless the cerebrates are not so much controlling the hive mind as providing a hub for communications and additional brain power. However, that means that killing cerebrates would not be the crippling blow it was in canon (which itself was only necessary because the narrative contrived to make the zerg unbeatable except by deus ex machina). Losing your communication hub and much of your intelligence would be terrible, but as we established in this argument the zerg are already intelligent enough to coordinate without it (albeit less efficiently since it clearly provides brain functions they don't already have) and even re-spawn it given enough time (as they do in the Retribution campaign).

So the zerg cannot be liberated into peaceful hippies or enslaved to the will of an infested terran with motives counter to the zerg's. Anything connected to their hive mind will automatically serve their genetic imperative to conquer the universe. The only way for an outsider to control them is to use psychotropics to disrupt their sanity so they can be directed in ways the controller desires. While this might work for a war or something, I can imagine so many ways it could go wrong if you don't exterminate the zerg after they served your purpose.

In any event, trying to devise a logically consistent explanation for the zerg group mind requires both ignoring and prohibiting the events of canon. It also helps to have a basic understanding of computer network topology because that is the closest analogue in real life to group minds.

Feel free to share your thoughts, critique, etc.