Children in Halachah by Rabbi Simcha Bunim Cohen has a fourteen-page chapter devoted to the laws of yichud. Three quotations that answer your questions:
A man may not be alone with a girl who is above three years of age; a woman is prohibited to be [sic] secluded with a boy over nine years of age.
However, in the Hebrew footnote he cites Rav Moshe Feinstein as saying that nowadays the prohibition on a man and girl's seclusion may start later and that, although he doesn't wish to permit it, he won't protest against those who allow such seclusion until a later age. That much is in Rav Moshe's Igros (Even Haezer 4, responsum 65 section 12); Rabbi Cohen notes in the footnote that he heard from Rav Moshe personally that in case of need one can be secluded with a girl until age seven.
The minimum age at which a girl may be considered a chaperon is a matter of controversy among the authorities. Some rule that the girl may be as young as three years old, while others require the girls to be five years old. Hagaon Rav Moshe Feinstein zt"l ruled that eligibility to be a chaperon begins at the age of seven.…
There is also a difference of opinion as to the age at which a girl may no longer be considered a proper chaperon. Some rule that the maximum age is nine, while others consider her a sufficient chaperon until she is bas mitzvah (twelve years old). It is best to be stringent in this matter, but in case of need, one may rely on the more lenient view.
The minimum age at which a boy may be considered an adequate chaperon is also disputed. Some Poskim rule that the boy must be five years old; however, Hagaon Rav Moshe Feinstein zt"l ruled that the minimum age is seven.…
The maximum age for a male chaperon is disputed as well. Some deem a boy as an adequate chaperon until the age of nine, while others permit the boy to be a chaperon until he is bar mitzvah (thirteen years old). In case of need, one may rely on the lenient opinion.