But as long as she has not received the get, she is still a married woman and can have relations with her husband, no? Regardless, it is also possible that they may decide to cancel the divorce, and in that case if she is not pure then there is a danger that they will violate the prohibition of niddah if quite a bit of time has already passed.

No. They are forbidden to have relations if they have decided to separate. She is a “divorced in his heart” wife. In the current situation there is no obligation at all to worry about some future change.

1. I found here – https://www.yeshiva.org.il/midrash/28486 – that according to the Geonim, “divorced in his heart” applies only in a case where the man did not inform his wife that he wants to separate from her (and that really does sound fairly logical). What does the Rabbi think?
2. Also, is there a difference if the husband himself does not want to separate, but the woman does, and in order not to “keep her by force” he agrees to divorce her?
3. Is the concern about children of a “divorced in his heart” wife actually a halakhic category (that is, the woman’s halakhic status is defined as “divorced in his heart,” which imposes certain restrictions on her and/or on her husband, etc.), or should this be treated as a scientific fact (mistaken?) that the Sages inferred – that in such a case, if he has relations with her, then the children will come out flawed for some reason?

Thank you.

1. The simple reasoning is that whenever he does not want to live with her, he is forbidden to have relations with her. If he did not tell her, that is an additional prohibition of hypocrisy.
2. In my opinion there is no difference, at least morally. And this whole discussion here is moral.
3. It is not because of some flaw in the children. The flaw (whether it exists or not) is a result.

2. Why is this whole discussion moral and not halakhic? Also, why is there no difference in this case? After all, the husband himself does want to live with her.
3. Could you please explain the parameters of the halakhic prohibition? From what I understood, the Sages defined that in a case where a man has relations with his wife when she has the status of a “divorced in his heart” wife, then children who are born may have some defect. If I understood you correctly, you are claiming that from the outset there is a restriction on marital relations with a woman in such a status, and an additional consequence is the creation of a defect in the children. If I understood you correctly, could you explain why you think that follows from the plain meaning of the Talmudic text?

2. If the woman does not want to live with him, the marriage is over. They have gone back to the state of betrothal. See my article: https://docs.google.com/document/d/0BwJAdMjYRm7IVUJJM29EY0syTHc/edit?resourcekey=0-uQiV6kBjUYbJGu2p2jTIpQ
3. In Gittin 90a it says:
Rav Mesharshia said to Rava: If his heart is set on divorcing her, and she sits under him and serves him, what is the law? He read concerning him: “Do not devise harm against your neighbor while he dwells securely beside you” (Proverbs 3).
That speaks about a case where he wants to divorce her and did not tell her.
But in Nedarim 20b the matter of a “divorced in his heart” wife appears, and in the plain sense, in my opinion, it is not connected to the question of whether she knows or not.
The fact that there is a flaw in the children is because there is something wrong with such relations. That is completely straightforward.