Is it permissible for a woman to arrange her own marriage or the marriage of another, and is the authorization written by the man to his wife for the marriage of their daughter valid if no one witnessed it and he later denied it?

A husband's authorization of his wife to arrange their daughter's marriage is permissible if the intention is to pave the way for the marriage, such as for engagement, agreeing on the dowry, and obtaining consent. However, the actual solemnization of the marriage contract is not permissible for a woman to perform. It was narrated that Aisha (may Allah be pleased with her) used to say, "Solemnize the marriage contracts, for women do not solemnize marriage contracts." This is well-known from the sayings of the Companions. Aisha's arrangement of Hafsah bint Abdur-Rahman's marriage was a preliminary step towards the marriage, not the solemnization of the marriage contract itself. If the husband denies authorizing the preliminary arrangements for the marriage, then the default is that it did not occur unless there is evidence. However, if the authorization was for solemnizing the marriage contract, then he has the right to insist on its invalidity.