The Gemara says that a father can tell his daughter who is a קטנה to go out and receive her Kiddushin from whomever she chooses. Tosfos says that it is not מדין ערב but rather that she has a יד to accept her own Kiddushin - ע"ש.
Question A: It is clear from the Gemara on :דף י"ח that a קטנה who marries herself off is not married when it says there that you can't call a girl an אלמנה when she married herself off ["?אלמנה קרי לה"]. So how can you say that a girl who chooses to accept Kiddushin from a man is married? [It can't be מדין שליחות because there is no שליחות for a קטנה].
Question B: If she is independent after her father gives her the green light, that means that she can marry even after his death. That is untenable!!?
Here is presented a Philosophical-Halachic-Tezler-Explanation [P.H.T.E. - everything today goes with Roshei Teivos.....] to this conundrum.
