Rambam - 1 Chapter a Day

These women are mentioned in Chapter l, Halachah 4.

In Halachah 5, with regard to relations with a woman in the niddah state, and in Chapter 7, Halachah 2, with regard to the Sabbath prohibitions, the Rambam writes that the days themselves constitute an interruption. In those instances, however, during the interim days, the prohibition did not apply (the woman returned to a state of purity and the Sabbath ended). Hence a distinction is made and every transgression is considered individually. In this instance, by contrast, the prohibition continues throughout all the days in the interim. Therefore, all of the transgressions are covered by the same sin-offering.
See also Chapter 6, Halachah 9, where the Rambam writes that if a person becomes aware of his different transgressions at varying times, he is liable for more than one sin-offering.

As stated in Halachah 3, were there to be different women involved, each transgression would require a different sin-offering. Nevertheless, in this instance, since only one woman was involved, he is liable for only one sin-offering.

I.e., between relations, she forgot about the prohibition.

The Rambam is emphasizing that although they engaged in the forbidden relationships together, since there is a difference in the extent of their awareness, there is a difference in the number of sin-offerings they are required to bring.

I.e., one for every act of intimacy.

Keritot 3a, cited in Chapter 4, Halachah 1.

Or was sodomized by both.

See Hilchot Gerushin, chs. 12-13, with regard to when such a woman is given license to remarry and when it is suspected that her husband is still alive.

Even if the court granted her permission to remarry, she is not considered to have sinned due to forces beyond her control. See Yevamot 87b, 92a, where this issue is discussed.

In which instance, unknowingly, every act of intimacy with her second husband was an adulterous act.

I.e., one after the other during the time she was under the impression that her first husband had died.

In this instance as well, unknowingly, every act of intimacy was an adulterous act.

I.e., throughout the entire time, he did not become aware of the prohibition involved in intimacy with her while she was in the niddah state.

He is not, however, liable for every time they were intimate. All relations during one span of time when the woman is in the niddah state are atoned for by one sin-offering (Keritot 17a).

As stated in Hilchot Issurei Bi’ah 4:9: “Whenever a woman has a fixed time when she is accustomed to menstruate, her husband can assume that she is [ritually pure and] permitted until she tells him “I am impure.”

In which instance, relations represent a transgression. See Halachah 7.

And hence must bring a sin-offering.

See Hilchot Issurrei Bi’ah 4:14, where the Rambam writes: It is the practice of Jewish men and women to carry out a personal inspection after relations. What is implied? The man should clean himself with a cloth prepared for [this purpose] and the woman should clean herself with a cloth prepared for [this purpose]. [The purpose of these inspections is] to see whether the woman menstruated during relations.
As mentioned in the notes to that halachah, the Shulchan Aruch (Yoreh De’ah 186:1) does not require a husband and a wife to carry out such inspections in an ongoing manner.

As stated in Hilchot Issurei Bi’ah 4:12: It is forbidden for a man to engage in relations with his wife near the time she can expect menstruation to begin, lest she menstruate during relations.... For how long [is it necessary to refrain from relations]? If [the woman] would ordinarily begin menstruating during the day, she is forbidden to enter into relations from the beginning of the day. If she would ordinarily begin menstruating during the night, she is forbidden to enter into relations from the beginning of the night.

It is not considered as a willful transgression, since the couple did not expect that she would become impure. Nevertheless, since the possibility existed that she would become impure, atonement is required.

For a man who engages in relations with a woman in the niddah state is also impure (Leviticus 15:24).

For it can be assumed that the blood came from the woman’s menstruation during intimacy. Even if he waited before cleaning himself, we have no reason to attribute the bleeding to any other source.

Since she waited, it is possible that she began menstruating afterwards and was not impure during the time of intimacy. Hence there is an irresolvable doubt whether they transgressed or not, for there is no way that this matter can be determined (Niddah 14b).

Since it is possible they are not obligated to bring a sacrifice, it is forbidden for them to do so, lest they be slaughtering an ordinary animal (i.e., an animal consecrated in error) in the Temple Courtyard, which is a transgression.

I.e., a longer interval.

Although there is a possibility that he contracted impurity, it is also possible that she began menstruating afterwards. Hence we assume that she was pure until bleeding was discovered and her husband is not deemed impure.

But instead, should remain within his wife until his erection becomes limp.

Hilchot Issurei Bi’ah 4:11.

I.e., with regard to his entry and his withdrawal. They are two different lapses of awareness: a) the thought that he could complete relations before she menstruated, and b) forgetting that it is forbidden to withdraw while erect.

Rav Yosef Corcus, Rabbi Akiva Eiger, and others note that here there is reason to say that the act should be considered as two transgressions, because he became aware of the prohibition between his entry and his withdrawal. Now, when one inadvertently engaged in two forbidden experiences of intimacy and became aware of the transgression in the interim, he is liable for two sin-offerings. Hence, there is room to say that he should be liable for two sin-offerings in this instance as well. Among the resolutions offered is that, here, the second forbidden act is so closely tied to the first that they are considered as being carried out in the same lapse of awareness (Or Sameiach).