Answer by isanae for Tolkien's history of Elves singing and Ents walking and talking

Ents were likely born at the same time as Elves

Elvish speech and song

The Elves awoke without speech or song:

By the starlit mere of Cuiviénen, Water of Awakening, they rose from the sleep of Ilúvatar; and while they dwelt yet silent by Cuiviénen their eyes beheld first of all things the stars of heaven.

^{The Silmarillion, Of the Coming of the Elves, p. 45}

They developed both before Oromë found them:

Long they dwelt in their first home by the water under stars, and they walked the Earth in wonder; and they began to make speech and to give names to all things that they perceived. Themselves they named the Quendi, signifying those that speak with voices; for as yet they had met no other living things that spoke or sang.

^ibid.

I could not find anything about the order in which they learned speech and singing. I would guess that they developed both concurrently, but I have nothing to support this.

Ents and Elves

Ents awoke at the same time as Elves:

And Manwë said: 'O Kementári, Eru hath spoken, saying: "Do then any of the Valar suppose that I did not hear all the Song, even the least sound of the least voice? Behold! When the Children awake, then the thought of Yavanna will awake also, and it will summon spirits from afar, and they will go among the kelvar and the olvar, and some will dwell therein, and be held in reverence, and their just anger shall be feared."

^{The Silmarillion, Of Aulë and Yavanna, p. 41}

Indeed, Ents were alive at a time when Elves had neither speech nor song.

Ents walking and talking

Ents were able to walk when they awoke. As quoted above:

they will go among the kelvar and the olvar

But also:

"In the mountains the Eagles shall house, and hear the voices of those who call upon us. But in the forests shall walk the Shepherds of the Trees.'

^{The Silmarillion, Of Aulë and Yavanna, p. 41}

As for talking, your quote seems to be satisfactory: although Ents could walk from the moment they awoke, they did not have speech. Elves taught them how to talk and sing.

Huorns

As for Huorns, they seem to be between Ents and trees:

"Some of us are still true Ents, and lively enough in our fashion, but many are growing sleepy, going tree-ish, as you might say. Most of the trees are just trees, of course; but many are half awake. Some are quite wide awake, and a few are, well, ah, well getting Entish."

^{The Lord of the Rings: The Two Towers, Treebeard, p. 77}

I couldn't find any mention of Huorns outside of The Lord of the Rings, so I don't think we'll be able to find a very precise definition. I would guess that Ents were Ents and trees were trees for a long time before Huorns appeared.

I would say they are of a form less mighty than Ents, but more so than trees. I guess you could say they are "devolved Ents" and "evolved trees" (even though evolution has nothing to do with this and "de-evolution" is certainly not a thing anyway).

^{All citations from the Harper Collins editions, all emphasis mine.}