1) A WOMAN WHO HAS A CHILD FROM A YISRAEL
QUESTION: The Gemara suggests that the verse, "Ki Siheyeh Almanah u'Gerushah" (Vayikra 22:13), teaches that when a Bas Kohen has children from a Yisrael she may not eat Terumah after her husband dies, but if she has children from an Eved or a Nochri she may eat Terumah, because the children from a non-Kohen with whom Kidushin cannot take effect do not disqualify her from eating Terumah. The Gemara rejects this suggestion on the grounds that if this would be the intention of the verse, there would be no purpose in the additional verse (the extra word, "u'Vas") which teaches this Halachah with regard to a Bas Yisrael or Bas Levi (since they do not eat Terumah even in their fathers' home).
RASHI explains that even if the Bas Yisrael or Bas Levi has a child from a Kohen and thus may eat Terumah (see 68b), there still would be no need for a verse to teach that if she then bears a child from a Yisrael she may no longer eat Terumah. Since the verse already teaches that a Bas Kohen may not eat Terumah because of her child from a Yisrael, certainly (Kal v'Chomer) a Bas Yisrael or Bas Levi may not eat Terumah when she has a child from a Yisrael. The verse is also not needed to teach that a Bas Yisrael or Bas Levi may eat Terumah when she has a child from a Nochri, because if a Bas Kohen may eat Terumah even though she has a child from a Nochri, certainly a Bas Yisrael or Bas Levi may eat Terumah in such a situation.
Why does the Gemara assume that a Kal v'Chomer teaches that a Bas Yisrael and Bas Levi become disqualified from eating Terumah because of a child born from a Yisrael? The Gemara earlier (68b) explains that there is more of a reason for a Bas Kohen to become disqualified than for a Bas Yisrael to become disqualified: a Bas Kohen has inherent Kedushah, and therefore relations with an "Ish Zar" can disqualify her more readily than it can disqualify a Bas Yisrael. Consequently, perhaps a child from a Yisrael disqualifies only a Bas Kohen from eating Terumah, while such a child does not disqualify a Bas Yisrael or Bas Levi, and thus the additional verse is still necessary.
Moreover, Rashi seems to rely on this logic himself when he writes that if a child from a Nochri does not disqualify a Bas Kohen from eating Terumah, certainly such a child should not disqualify a Bas Yisrael. Rashi implies that it is easier for a Bas Kohen to become disqualified than for a Bas Yisrael to become disqualified! Why, then, does the Gemara say that no verse is necessary to teach that a child from a Yisrael disqualifies a Bas Yisrael and Bas Levi from eating Terumah? (MAHARSHA)
ANSWER: The MAHARSHA answers that a Bas Kohen can become disqualified easier only through an act which directly contradicts her Kedushah. For example, the Gemara (68b) says that a Bas Kohen who has relations with a man to whom she is forbidden detracts from her Kedushah, and thus in such cases it indeed is easier for her to become disqualified. Similarly, if she has a child from an Eved or Nochri, since the child was born through an act of prohibited relations, it should affect her more than it would affect a Bas Yisrael or Bas Levi.
However, if a Bas Kohen has a perfectly legitimate child from a relationship with a Yisrael (a completely valid relationship), the fact that her child from a Yisrael disqualifies her from eating Terumah in no way detracts from her Kedushah. Rather, it is merely her connection to a Yisrael through the child that removes her right to eat Terumah. Accordingly, the Gemara is justified in its assertion that in such a case a Bas Yisrael and Bas Levi certainly lose their rights to eat Terumah for that reason.
2) THE STATUS OF A WOMAN WHO MARRIES HER "MACHZIR GERUSHASO"
QUESTION: RASHI (DH v'Eima Niv'alah) cites a Beraisa (44b) that states that when a man remarries his ex-wife (in a case of "Machzir Gerushaso"), "she is Kesherah and her child is Pasul." Rashi explains that she is Kesherah to marry a Kohen, and certainly she may eat Terumah.
How can she be Kesherah to marry a Kohen? She is a Gerushah (divorcee), who is prohibited to a Kohen! (MAHARSHA)
(a) The MAHARSHA answers that Rashi's words, "Kesherah l'Kehunah," refer to the daughter born from the union. When the Beraisa says that the woman herself is Kesherah, it refers only to her rights to eat Terumah, as Tosfos writes (44b, DH Hi).
(b) The ARUCH LA'NER (44b) explains that Rashi does not mean that the woman may actually marry a Kohen, but rather he means that the woman is not a Zonah.
Why does the Beraisa say that she is "Kesherah" if she is not really fit to marry a Kohen? The Aruch la'Ner explains that the Chachamim in the Beraisa are responding to Rebbi Akiva. Rebbi Akiva says that a woman who has relations with her husband who is "Machzir Gerushaso" becomes Pesulah. This means that aside from her status of a Gerushah which disqualifies her from marrying a Kohen, she also attains the status of a Zonah. The Chachamim reply that "she is Kesherah" -- she does not attain the status of a Zonah.
(Alternatively, the Chachamim use the word "Kesherah" in order to express their disagreement with Rebbi Akiva in a number of cases. One of those cases is "Kerovas Chalutzaso," a woman who is neither a Gerushah nor a Chalutzah and is not prohibited from marrying a Kohen. Since it is appropriate to say that such a woman is Kesherah to marry a Kohen, the Chachamim say "Kesherah l'Kohen" (and is not a Zonah) with regard to all of the cases in which they disagree with Rebbi Akiva, even though the woman in the case of "Machzir Gerushaso" indeed is disqualified from marrying a Kohen because of her separate Pesul of Gerushah.)
Why does Rashi insist on explaining that she is Kesherah "l'Kehunah" and not "l'Terumah"? Rashi apparently follows the logic of his first explanation earlier (68b, DH Iy Hachi). He maintains that a Zonah is not disqualified from eating Terumah but only from marrying a Kohen. When Rebbi Akiva argues and says "she is Pesulah," he must mean that she is a Zonah and may not marry a Kohen, and when the Chachamim argue and say "she is Kesherah," they mean that she may marry a Kohen. (See Insights to Yevamos 68:2:a.)