One of your questions is at the center of much rabbinic discussion, whereas the other is apparently not. But both are good questions and may even help answer each other. First, let us see if all of your assumptions are correct.
The gemara[1] treats zechirat yetzi’at Mitzrayim as a mitzva from the Torah, and the mishna[2] cites a pasuk as a source for it: “in order that you will remember the day that you left Egypt all of the days of your life.”[3] We also seem to accept Ben Zoma’s opinion[4] that we must fulfill this mitzva both day and night.[5] Therefore, the Magen Avraham[6] says, since zechirat yetzi’at Mitzrayim is a Torah law that applies every day, at any time of day, it is not time-based and women are obligated to fulfill it. The Sha’agat Aryeh[7] counters that there are actually two different obligations, of the day and of the night, and each one is time-based. Therefore, women are exempt from each obligation. The Mishna Berura[8] presents both opinions, but the minhag seems to be that women are exempt.[9]
If zechirat yetzi’at Mitzrayim is from the Torah, why then is it not included in the list of the 613 mitzvot? (The Semak does count it,[10] but most do not.) Several explanations are given. The Ohr Samei’ach[11] suggests that zechirat yetzi’at Mitzrayim, as an independent mitzva (as opposed to a desired result of the performance of other mitzvot), may be only rabbinic. The scriptural source mentioned above that implies that this mitzva is from the Torah can be explained to mean that it is evident from the Torah that HaShem is interested that we remember the Exodus. Therefore, Chazal treated the daily practice to do so as if it were Torah law. Similarly, the Tzelach[12] says that the Torah source cited is a valid Torah source, but since it is not written in the form of a command, it is not counted.
We present one more explanation, which will help deal with your other points as well. The Beit Yitzchak[13] says that the Rambam viewed zechirat yetzi’at Mitzrayim, not as an independent mitzva, but as something we are to do along with the mitzva of Kri’at Shema. Therefore, he adds, since women are exempt from Kri’at Shema, they are also exempt from the addendum of zechirat yetzi’at Mitzrayim.
Finally, let us deal with the question of why women aren’t obligated, in spite of their involvement in the miracles of the Exodus. The gemara does refer to this justification for women’s obligation in a few places, including when discussing the obligation of women to drink the four cups of wine on seder night.[14] However, we did not find that those who discuss the obligation or exemption of women in zechirat yetzi’at Mitzrayim consider this factor. One can give some technical answers. For example, Tosafot[15] cites an opinion that holds that af hein hayu b’oto haness applies only to rabbinic commandments, not to Torah ones.[16] Therefore, this reasoning would not suffice to obligate women in the Torah commandment of zechirat yetzi’at Mitzrayim.
The following, fundamental approach seems to give a better understanding. The Minchat Chinuch[17] and others deal with the practical issue of why we need a mitzva to discuss yetzi’at Mitzrayim on seder night if we mention it every night anyway. Conceptually there is a major difference. On seder night, the focus of the mitzva is to praise HaShem for the miracles that saved us years ago at that time of year. During the rest of the year, it is primarily a matter of stating fundamental beliefs, that the Lord who did miracles and redeemed us is One whom we should believe in and obey.[18] For that reason, we perform the mitzva by mentioning the Exodus along with other principles of faith contained in Kri’at Shema. In that context, one’s involvement in the miracles, which mandates praise, is not the critical point. Thus af hein hayu b’oto haness does not obligate women in this mitzva.