Rambam - 1 Chapter a Day

This refers to an instance where one pours impure water into a mikveh. See Halachah 5.
Compare to Hilchot Ma’achalot Assurot 12:12 which states with regard to wine associated with idolatry that a column of wine being poured is considered as connected to the lower container. That, however, is a unique stringency resulting from the severity of the prohibition against benefitting from such wine.

We do not say that since the object into or onto which it is being poured is impure, the impurity flows up the entire column. Rather than considering the column as a single entity, each portion is considered as separate [see the Rambam’s Commentary to the Mishnah (Taharot 8:9)].

The liquids are considered as a primary derivative of impurity. They impart impurity to the container in which they are held.

Thus it is considered as if liquids from the bottom container mixed with those of the upper container and imparted impurity to them.

Nevertheless, as the Rambam explains in his Commentary to the Mishnah (Machshirin 5:10), when the liquid one is pouring is hot, even if the bottom one is hotter, the vapors from the bottom container do not have such an effect on the liquids being poured.

I.e., because vapor from a hot pot is considered as connected to a cold entity above it.

In which instance, they would contract impurity, as stated in Hilchot Sha’ar Avot HaTum’ah 8:1.

Even if none of the liquid that collected on her hand dripped back into the pot.

These refer to the names of places in Eretz Yisrael, as stated in the Rambam's Commentary to the Mishnah (Machshirin 5:9). In his notes to that mishnah, Rav Kapach cites Joshua 15:24, 55 which mentions two places referred to as Zif; hence, the use of the plural. The commentaries have noted that they have not found a place called Tzapachat.

If one touches the honey and then withdraws his hand, some of the honey will ascend with his hand and remain extended between his hand and the honey. See Nazir 50b.

I.e., their honey is very thick; hence, it is considered as a single entity and by touching one portion, one is considered to have touched the entire amount.

Halachot 1 and 2 above.

I.e., a container that is not susceptible to ritual impurity. If the container was susceptible to ritual impurity, there would be no question that the water being poured would be considered as impure. For even if the water being poured were considered as connected to the mikveh, it would still be considered as impure. For the container would have contracted impurity from the liquids. It would then continue to impart impurity to them, counteracting the influence of the mikveh.

Chapter 2, Halachot 21-22.

That would cause liquids poured on it to flow down quickly [the Rambam’s Commentary to the Mishnah (Taharot 8:9)].

It appears that the other liquids were collected to the extent that they can be perceived as an independent entity, not merely felt as moisture.

If the liquid collected at the bottom is impure.

If the liquid collected at the bottom is a mikveh.

Impure food does not impart impurity to other substances unless it is the size of an egg-sized portion. Now, the three pieces reach that size only when combined. Thus the question is: Are they considered as combined or not? If they were considered as combined, they would impart impurity to the liquids which would in turn impart impurity to the kneading trough [the Rambam's Commentary to the Mishnah (Taharot 8:8)].

This is speaking about pieces of dough [or other foods] that are next to each other, but not attached to each other. The water does not cause them to be considered as combined, because, as stated in the previous halachah, water on an incline is not considered as a single unit. Hence, the drop of water between the upper two pieces is considered a separate entity from the drop between the pieces.

That together would comprise an egg-sized portion.

For there is one drop of water between them. That drop of water is touching an egg-sized portion of impure food.

Not just moisture that could be felt, but a collection of water that was not flowing.

Thus if all the small pieces together comprise an egg-sized portion, they impart impurity. The Kessef Mishneh interprets the measure of mustard seeds as referring to the water. If there is a mustard seed’s amount of water on the kneading trough, the pieces are combined. Rabbenu Asher, Rav Ovadiah of Bartenura, and others (Taharot, op. cit.) interpret the term as referring to the pieces of food: Even if they are as small as a mustard seed, the liquid can combine them.

Hilchot Sha’ar Avot HaTumah 10:2-3.

Such a person is referred to as a t’vul yom. He is still ritually impure until nightfall. Nevertheless, since he has already immersed, the degree to which he imparts impurity is reduced, as stated in the following halachah.

Causes them to be considered impure, but not to impart impurity to others. This applies even to the liquids. Although generally, liquids are always considered as primary derivatives, an exception is made in this instance.

See the following chapter.

I.e., it merely stems from a Rabbinic decree. See Hilchot She’ar Avot HaTumah 8:10-11.

I.e., he has done everything required of him and the requirement for his purification will come inevitably. See Hilchot Pesulei HaMukdashim 18:14 which mentions another leniency which, according to the Rambam, applies with regard to a person who immersed during the day but did not wait until nightfall.

T’vul Yom 1:5 mentions other foods in this category as well. The Kessef Mishneh questions why the Rambam does not include them. The commentaries explain that in Chapter 1, the Rambam excluded these foods from all types of ritual impurity, because they are not considered as designated for human consumption.

Barley and spelt are often used for animal fodder. Hence, when they are not shelled, leniency is granted. Wheat, by contrast, is almost exclusively used for human consumption. Therefore the laws are more stringent. See also Chapter 5, Halachah 12, where a distinction is made with regard to the shell itself.

See Chapter 5.

See Chapter 6, Halachah 9.

See the following chapter.

See Hilchot Sha’ar Avot HaTum’ah, ch. 8, with regard to the impurity of hands. Although both a person who immersed that day and impure hands only disqualify terumah and do not empower it to impart impurity, there are certain differences between the two.

See Hilchot Sha’ar Avot HaTum’ah 10:5 which mentions another such stringency.