Shouldn't Changelings be entirely genderless?

[Uxi]

So, if the changelings are really just one big creature, then the idea of having children really doesn't have any meaning. Really, the Great Link as a whole just grows new goo as it gets older. And when necessary it can send off parts of itself for short (or long) times which act autonomously, but are not really a different entity per see.

That's an interesting theory and seems to fit. I was thinking the minds merged while the piles of goo were semi distinct (to account for the brainwashing (though that seemed to fade with time) but I like that one better.

And if this was the case, just how many autonomous units or beings could the Great Link break into? Could Odo break himself apart into 2 or more independent Odos, initially having the exact same personality, but each being able to go off and have independent lives and result in divergent beings?

This idea makes sense. And it's an interesting sci-fi concept. But really it doesn't hold up in the show. At no time did we get the sense that Odo's sub-parts could operate independently (at least nothing more than moving to come together to form the whole Odo again). And when Odo entered and left the Great Link there was no evidence to support the idea that his personality had changed at all to be more like the general changeling personality.

Odo was limited, though, and had to learn everything by trial and error. After he went in the Link the first couple times, he got better (able to duplicate the Female and presumably individuals with more practice). Maybe he just never learned how to "split" (and/or once he did never really had the opportunity/need. Some of the times when he could have used it, he was infected by the morphogenic virus which could have prevented it.