Rambam - 1 Chapter a Day

I.e., far removed from him, but in a place and at a distance where the rider can see the person with the flags clearly.

All these particulars are mentioned so that if a person was present at that place, at that time, and did not see the crime take place or was with the witnesses in another place at that time, he could come to court and nullify the testimony that served as the basis for the conviction.

I.e., even if the people who accompany him feel that his words are not substantial, they bring him back to the court. Since he is brought back to the court regardless, scholars who can evaluate the substance of his words are not sent with him the first two times (Sanhedrin 43a).

In his Commentary to the Mishnah (Sanhedrin 7:3), the Rambam explains that the execution is placed in the hands of the witnesses, because they are the only ones who have firsthand knowledge of the transgression. Since everyone else knows only because of them, they are given the responsibility to carry out the execution.

One of the four types of death: stoning, burning, decapitation, or strangling.

As Deuteronomy 17:7 states: “And the hand of the witnesses shall be the first against him.”

With regard to others condemned to death, by contrast, it is the witnesses who must execute them. See Halachah 7, and Chapter 14, Halachah 8.

We fear that if he is asked to confess at the place of execution itself, he will be overcome by fear and will not be able to confess properly [the Rambam’s Commentary to the Mishnah (Sanhedrin 6:2)].

For certainly he has other sins, for which he is liable.
Sanhedrin 43a suggests that, in such a situation, a person should say: “May my death be atonement for all my sins except this one,” It, however, rejects that option lest all the executed adopt that version to create the impression that they were framed.
Significantly, in Sefer HaMitzvot (positive mitzvah 73), the Rambam writes that if a person knows that he is being framed, he should not confess. Mayim Chayim explains that in Sefer HaMitzvot, the Rambam is speaking according to Scriptural Law, while here he is speaking according to Rabbinic decree.

But not before, so that he will be of sound mind when he confesses (Torat Chayim).

I.e., he is not required to face his death with a clear mind. Sanhedrin 43a draws support from Proverbs 31:6: “Give strong drink to one who is lost and wine to the bitter of soul.”

See Chapter 15, Halachah 1.

Ibid.:4.

Ibid.:5.

Ibid.:7.

See Halachah 1.

Sanhedrin 43a states that “the precious women of Jerusalem would donate the wine and the frankincense.”

This might create the impression that the court desired to see him executed (Sanhedrin 43a).

See Chapter 18, Halachah 3, and notes which explain that this interdiction includes within it several prohibitions involving different subjects.

The meal brought to the mourners after the burial. See Hilchot Evel 14:9.

Sanhedrin 63a states that this act diminishes the honor of the executed person and thus helps bring him atonement.

As stated in Chapter 18, loc. cit., this prohibition is considered as being “inclusive in nature.” Although all of the forbidden acts included within it are forbidden by Scriptural Law, nevertheless, because of the general nature of the prohibition, their violation is not punishable by lashes. See Sefer HaMitzvot, General Principle 9.

Since Chol HaMoed are festive days, it is improper for the judges to be forbidden to eat. Hence the judgment is prolonged. Since the sentence was not delivered, this is not considered as prolonging the condemned person's suffering.
The implication is that the judges are permitted also to drink wine. Although they have not delivered their ruling and a person who is intoxicated is forbidden to deliver a ruling, no restriction is given. Some suggest that since they have already made their decisions and the hesitation in delivering the ruling is merely a technical factor, there is no necessity for a restriction. Kin'at Eliyahu suggests that the awe of dealing with a case involving capital punishment will prevent them from losing self-control.

As mentioned above, this failure to show them respect conveys atonement upon them (Sanhedrin 46b). In his Commentary to the Mishnah (Sanhedrin 6:8), the Rambam writes that the atonement for these individuals is not granted until their corpses begin to decompose. Hence at the time of the funeral, it is not fit to mourn for them. See also Hilchot Evel 1:9 where this law is repeated.

Aninut refers to the severe feelings of mourning - and appropriate practices - experienced on the day a close relative dies. There is a difference of opinion among the Rabbis whether aninut applies only up until the burial or afterwards as well. From Hilchot Bi'at HaMikdash 2:9, it would appear that the Rambam maintains that the classification of aninut applies after the burial as well.
There are two contexts in which aninut is mentioned in the Torah: the prohibition against partaking of sacrificial offerings (Leviticus 10: 19) and the prohibition against partaking of the second tithe (Deuteronomy 26:14). Other mourning practices associated with aninut are mentioned in Hilchot Evel 4:6.

These feelings do not detract from the atonement to be granted the person executed.

See also the following halachah.

For if he is not executed by the witnesses, the entire Jewish people are obligated to execute him (Sanhedrin 45b).

As Deuteronomy 17:7 states: “And the hand of the witnesses shall be the first against him.” See Halachah 1 and Chapter 14, Halachah 8.

For only such a court may deal with cases involving capital punishment.

This refers to a court of judges who received semichah in Eretz Yisrael, but who were found in the diaspora either temporarily or permanently (Chapter 14, Halachah 14).

Maybe the merit of Eretz Yisrael will make it possible that a rationale to acquit him will be found (Makkot 7a).

For once they judged him and sentenced him to death, there is little likelihood of them changing their minds.