The Citadel is an archive of information for George R.R. Martin's A Song of Ice and Fire.
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Yet if every knight can create a knight as we have seen in "The Hedge Knight", what prevents a widespread misuse by unscrupulous hedge knights such as Ser Osmynd Kettleblack or the cynical Great Houses?
Social pressure. A knight's peers would look with a certain amount of disfavor on anyone who did this. They might gain money, but they would lose honor. And honor is still very important in this culture.
I.e. why didn't Ser Osmynd knight people for money, or at least why didn't he knight his brothers? And why are there members of lordly Houses, who aren't knights, i.e. (late) Gerion Lannister, Willas Tyrell, Alekyne Florent, numerous Freys, if they could be easily knighted by their relatives?
In a medieval culture, knighthood is not simply an honor, like when Queen Elizabeth knights Elton John in our world. It's a job, a profession of arms. You need to have a certain amount of wealth, enough for armor and a warhorse at the minimum, and there are obligations as well. You're expected to fight, to respond to the summons of your lord, to train and lead a group of men-at-arms. Certain people simply aren't capable of all that (Willas Tyrell, Samwell Tarly), and are better fitted to be septons, maesters, or simply lords on their estates. Others don't have the interest. Knighthood was also in part religious, and for that reason followers of the old gods don't tend to be knighted, thought they otherwise fit the bill.
And why did Lord Frey ask _Robb_ to see about Olyvar's knighting, when he had more than enough anointed knights at his disposal to attend to the matter?
Why should someone go to Harvard when they can get a degree from their local community college? There is great prestige in receiving your knighthood from a king, a prince, one of the Kingsguard or other celebrated, legendary knights. Getting knighted by a brother is like kissing your sister (we'll leave Jaime Lannister and the Targaryens out of that comparison) and getting dubbed by the local hedge knight is like graduating from barber college. You get a sheepskin, maybe, but don't try applying to law school.
Also, can noble bastards be knighted?
Any man can be knighted.
And how comes that the Manderlys have squires which are forty years old?
We tend to think of squires as teenaged boys, knights in training, but that is only part of the truth. Historically, there were many men who spent their entire lives as squires, and never became knights.It was quite common to have thirty- and forty-year-old squires, even some in their fifties. Such men perhaps did not have the wealth to become knights (knights had to pay for their own equipment), or perhaps did not have the inclination. They were the medieval counterparts of the career army sergeant who has no desire to be promoted to lieutenant. let alone general.