We learn from Mishpatim that a father can sell his daughter into the service of a master. This master then designates her as a future bride for himself or his son.
At what age is the maidservant married to the master or his son and is she allowed to refuse the marriage?
I assume she has the right to divorce once she is married (correct me if I'm wrong) so I'm wondering if she could refuse the marriage rather than wasting everyone's time if she thinks it's not a good match.
The principle of mi'un is well established in halachah, but it primarily applies to an orphan(ette) sold by their adult siblings or mother - there is another case where the father marries off a daughter who subsequently became widowed or a divorcee while still a minor. If he marries her off a second time, that marriage would potentially be subject to mi'un once she becomes of age.
The father has the right to marry off a minor daughter. Such a child is fully married and requires a get in order to be separated from their spouse. What Mishpatim adds is that when a person "buys" a minor Jewess as an eved, they are also purchasing the rights to marriage, either for themselves or for someone else in their family. While the daughter might verbally refuse to accept the kiddushin, her father can (or already has) accepted it on her behalf through the principle of Zachin Le'Adam Shelo Bifanav, coupled with the assumptions that 1) as a minor she doesn't have proper da'as to make an informed decision and 2) as a woman it is preferable to be married than single (Tav limeitav tan do milimeitav armelah).
The marriage initiates whenever the "master" decides he wishes to be married to her or to marry her off, but they must do so by the time she reaches maturity. If they fail to arrange a marriage after the daughter becomes an adult, then she regains possession of herself when her father loses the right to sell her off. It doesn't preclude her from getting married to her erstwhile owner, but now she has complete choice in the matter.
Since all divorce must be voluntarily initiated by the husband, the wife technically does not have a "right to divorce," though Beis Din is capable of "forcing one" out of her recalcitrant husband. (Babylonian Talmud, Arachin 21a; Rambam, Mishna Torah, Hilchot Gerushin, 2:2)
