How old are the maesters?

I haven't read the WB and don't know the context at all, but naming them pets (an term used by Yezzan for some of his slaves), their chains, and Tarly's attitude towards their servitude just makes me think of them as slaves.

Indeed. I believe that eventually we will be provided with some sort of historical connection between slavery and the various orders of service we've seen which require the permanent forfeiture of all familial inheritance.

Reading this, it occurred to me that maesters and citadel are exactly like the weirwood net, they also have a "face" every where. They imitate the flow of information with ravens which is ironic given their affinity to weirwoods.

We also have Varys's little birds (which I still believe are named after BR's Ravens), they operate the same way. What makes this analogy even more interesting is that Varys makes the little birds mute just like the ravens these days.

You are right, there isn't. But in the epilogue of the aDwD, the two kids that Kevan encounters (which I assume are two of little birds) and the other kids with knives are completely silent. They do not talk or make any noise. He never notices them missing a tongue, but it just reinforces their condition:

Notice how the boy never says anything to Kevan.
Also the girl observes no ceremony, she just points. She is talking to the hand of the king and still nothing.
Again, the only sound is of their soft movements, no talking.
Of course none of this is definitive, as you pointed out, but reinforces the idea.

And yes, generally what is the point of using the kids? They are the easiest to intimidate and I think if it comes to questioning them, they will crack the easiest. Also, kids probably lack the insight to know what is important and what is not. So, the whole premise makes little sense.

I think I have read some theory that Varys is skinchanging into the little birds to get info which would make it more like BR and also makes more sense especially if they are not in the same city. How are they sending messages? How come no one ever infiltrates Varys's info network?

The fact that Varys requires literacy in his little birds may account for a large number of missing noble children.

I'm thinking this one is primarily a matter of necessity. Aside from official names and titles, the ability to read is about a clear a mark of social distinction as you can find in the Seven Kingdoms. As has been demonstrated in-story with the likes of Jon Snow and (f)Aegon, in the chaos of war, the fates of even noble children are often neglected for want of presently capable decision-makers. The only reason anyone cared about Tyrek Lannister's disappearance with all the other chaos in the city is likely because he was just about old enough to wield a sword in combat. I could easily see Varys taking advantage of this neglect to collect forsaken recruits and re-program them, young and impressionable as they are, to act as his servants. We can probably throw some noble bastards who eventually wore out their welcomes into this pot as well. Speculation, I know, but there are a lot of lords and a lot of bastards out there, so it seems inevitable that some will be welcomed at first only to be thrust aside when they become an inconvenience (*cough cough* Jon Snow). Some might argue that the children young enough to be taken in this manner are also too young to read yet. However, we've already seem some demonstrable, though incomplete, re-programming of children as old as 9-12 in Arya Stark with the Faceless Men and Theon Greyjoy as Eddard Stark's ward.

This such method also echoes the Free Folk practice of not naming children until they reach two years of age. We even see this in the Seven Kingdoms, where, IIRC, noble lords generally don't trust the security of their bloodline until they have a trueborn son reach reproductive age himself. Parents are afraid to commit familial status to their infants for fear that they will be "spirited away" while they are still young enough to be re-programmed by new masters.