As the Macmillan English Dictionary definition says, a brainchild is "a clever system, organization, or plan that someone thinks of and develops". For example:
The plan is the brainchild of Divisional Officer Jim Smith.

The idea behind the metaphor is pretty clear I think – something clever that you invent is the child of your brain, just as a flesh-and-blood child is the child of your body. Brainchild is generally used in the singular, although you will find examples of brainchildren especially in journalism and the philosopher Daniel C. Dennett has written a book with the title Brainchildren. In normal everyday use there is almost always some kind of possessive marker to say whose idea the brainchild is:

His latest brainchild is a collection he describes as "contemporary clothes – grown-up and sophisticated."

... just students whose brainchild is now worth $72 billion.

The Festival Of Walking is the brainchild of organisers Margaret Wasem and Sheila Perry.

I am studying the use of the pronoun they as a generic pronoun. I was wondering if you could tell me, if it's possible, when this pronoun was included in an English dictionary with that meaning, that is, to replace the generic he.

I can't really answer this question directly as that would involve searching through dozens of English dictionaries until you found one that didn't include the use of they as a generic singular pronoun. What I can tell you is both that this usage has been around for a very long time and that it continues to arouse strong feelings. Even though the New Oxford Dictionary of English (1998) points out in a usage note that they has been used as a generic singular pronoun since the 16th century, and the Oxford English Dictionary gives many examples of its use from the works of a wide range of great English writers, many people still feel that it is incorrect, especially when it refers to a noun that is obviously singular.

The New Oxford English Dictionary in its note points out that the use of they (as well as them, their etc.) as generic pronouns became more widespread in the late 20th century as a way of deliberately avoiding the sexist he, his, him etc. or the cumbersome he or she. All modern dictionaries accept this use of they as current usage, though they vary in their degree of acceptance of it. Many, like the Macmillan English Dictionary, add a note saying that although the use is widespread, especially when referring back to a pronoun such as anyone, everyone, or someone, some people regard it as incorrect and so it should be avoided in formal writing.