In the show we see that one of the children of the forest
was there to turn the night king
Do we know their maximum age? also can they have children?
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No we do not know of the maximum age of the Children of the Forest.
We know the life span of at least one Child of the Forest which we can use as a reference point:
Meera said, "You speak the Common Tongue now."
"For him. The Bran boy. I was born in the time of the dragon, and for two hundred years I walked the world of men, to watch and listen and learn. I might be walking still, but my legs were sore and my heart was weary, so I turned my feet for home."
"Two hundred years?" said Meera.
The child smiled. "Men, they are the children."
ADWD - BRAN II
Since she says she was born when Dragons ruled and has lived at least for 2 centuries, that will make her date of birth in King Jaehaerys I's reign. And needless to say, now we know at least some of them can live upto 2 centuries and perhaps more given how healthy and young Leaf looked at that time. Or we can simply say that their lifespans are much longer than ours and leave it at that.
As for reproduction, yes they certainly can albeit at a slower rate than humans. They don't just simply pop out of the ground. In the Dawn Age, there lived only the elder races in Westeros which were the Children and the Giants. Eventually, the First Men started pouring in from the land-bridge that connected Westeros to Essos. And with that migration, came the wars between the children and the First men. With the tide turning against them, the children turned to desperate weapons and used magic to smash the land bridge connecting the two continents, called the Arm of Dorne. But it was too little and too late since Thousands of First Men were already in Westeros and more importantly, Wives of the First Men bore children more faster than the females of the Elder races which skewed the balance further in favour of men until the children were forced to realise that they could not win this war.
Most of what we do believe of the Breaking comes to us through song and legend. The First Men crossed from Essos to Westeros by land, all agree, walking or riding across through the hills and forest of the great land bridge that connected the two continents in the Dawn Age. Dorne was the first land that they entered, but few remained, as we have chronicled; many and more pressed on northward, through the mountains and mayhaps across the salt marshes that once existed where the Sea of Dorne is now. As the centuries passed, they came in everincreasing numbers, claiming the stormlands and the Reach and the riverlands for their own, eventually reaching even the Vale and the North. They drove the elder races before them, slaughtering giants wherever they found them, hewing down weirwood trees with their bronze axes, making bloody war against the children of the forest.
The children fought back as best they could, but the First Men were larger and stronger. Riding their horses, clad and armed in bronze, the First Men overwhelmed the elder race wherever they met, for the weapons of the children were made of bone and wood and dragonglass. Finally, driven by desperation, the little people turned to sorcery and beseeched their greenseers to stem the tide of these invaders.
Most scholars do agree that Essos and Westeros were once joined; a thousand tales and runic records tell of the crossing of the First Men. Today the seas divide them, so plainly some version of the event the Dornish call the Breaking must have occurred. Did it happen in the space of a single day, however, as the songs would have it? Was it the work of the children of the forest and the sorcery of their greenseers? These things are less certain.
No more wanderers crossed to Westeros after the Breaking, it is true, for the First Men were no seafarers...but so many of their forebears had already made the crossing that they outnumbered the dwindling elder races almost three to one by the time the lands were severed, and that disparity only grew in the centuries that followed, for the women of the First Men brought forth sons and daughters with much greater frequency than the females of the elder races. And thus the children and the giants faded, whilst the race of men spread and multiplied and claimed the fields and forests for their own, raising villages and forts and kingdoms.
TWOIAF - Dorne: The Breaking