Is the great link only "one person"?
As i recall from the episodes; a changeling who 'returns' to the Link is fully immersed - mentally and physically within the Link - one is all, all is one. When an individual emerges the Link 'programs' him with all the appropriate memories et al.
Or is it more like a 'hive mind' where the individuals make up the whole, but connecting to the Link sort of enhances that hive mind, but inside the Link is still made up of (thousands? millions? billions?) of individual Changelings?
And how do Changelings give birth?
My money is on the hive mind. Something like a group Vulcan mind-meld.
Let's look at Odo, even after several joining in the Great Link, he still lack some Changeling abilities, and the Changelings in the Link were able to lie to him and feed him false information.
Also the Female Changeling always take the same form, which would indicate that the Changelings are individuals.
As to reproduction.
In the novels we had the Progenitor, a giant Changeling that supposedly sired all the Changelings of the Great Link and/or the Great Link itself. And the Changelings themselves were supposedly immortal, but infertile.
Which may seem strange as we know there were 100 infants just a while ago. Do we actually known when the infant Changelings were sent out?
My take is that the Changelings actually reproduce through a form of mitosis. As a Changeling grows older and more experienced, they gel form increases in volume.
So at a point of time, the Changeling can detach a part of itself.
We have seen that when a part of of a Changeling is separated, it dies off. But I would say that a critical mass/energy is required for a Changeling part to develop a separate morphogenic matrix, an intelligence, a spark of life.
That is how I think the 100 infants were created, the existing Changeling gave a part of themselves to make up a 100 infant Changelings.