Oleksandr wrote:1) How samanera ordination was established?
The Buddha ordained Rahula, his son, and his father (the Buddhas, Rahulas grandfather) complained that he lost two people dear to him
2) Was it designed especially for children? If Buddha had banned children from becoming bhikkhus (because they could hardly bear ascetic lifestyle), why he let them ordain as a samanera? Then, what is the essential difference, making samanera ordination available for children?
he didn't ban it as such, he agreed that a better course of action would be to give them a lesser ordination.
3) May an adult ordain as samanera according to Pali canon and the Commentary? Were any such cases registered at that time? If no, when and why the practice of "adult samaneras" emerged?
Yes, and all bhikkhus ordain as novices first, sometimes the two ordinations are done one after the other (litterally), other times a few weeks or days are between the ordinations, and other times they stay as novices, not everyone feels the need to take full ordination, this is more common in the west, or Sri Lanka than Burma & Thailand.
4) Why samaneras are not asked about permission of their parents? Was it because it went without saying that they have it? Could a run-away kid become a samanera?
They don't need to ask because they aren't bound by the same rules, they have allot of freedoms Bhikkhus & Bhikkhunis don't have, so can reletavely live a closer to normal life than full monastics, they have only really taken on 1 extra precept, that of relinquishing money, but the rest are the same as a Upasaka/Upasika, although they tend to follow the 75 training rules aswell, many of which wouldn't inhibit a lay life, and I believe lay Dhamma Teachers follow these as well.
Someone else may correct anything I have erred on here, but I believe this is essentially correct without looking up the relevant stuff! but there is a section in the Buddhist monastic code 2 which may answer this last question more (chapter 9 if I remember rightly)