1. As explained in the preceding Halakhah, the Court does not bring a sacrifice for a false ruling in a case subject to a sacrifice which depends on the wealth of the person. These are enumerated in Lev. 5:1–4; the Mishnah uses the biblical expressions to characterize the different categories.
“Hearing of a voice” refers to Lev. 5:1: If a person sin, for he heard the sound of an imprecation when he is a witness, or saw, or knew; if he does not tell he has to bear his iniquity. If a person is asked by another to testify in his case before the court; he refuses and assents to an oath to the effect that he does not know about the case, if that was a lie he is subject to the variable reparation offering for swearing falsely.
“Expression of the lips” (v.4) refers to an oath made by a person on his own initiative but not kept since he forgot about his own oath. This also subjects the maker to the same obligation.
Improper handling of impurity because of oblivion is mentioned in vv. 2–3.

2. He is identified with the king.

3. Mishnah Sanhedrin 2:3. He extends the rules created for the non-Davidic kings to all kings.

1. Lev. 14:21. This is a wrong quote since it refers to the sacrifice of the healed sufferer from skin disease. The expression used in Lev. 5 is וְאִם⁠־לֹ֨א תַגִּ֣יעַ יָדוֹ֮ “if it is out of his reach” for the poor person and וְאִם⁠־לֹא֩ תַשִּׂ֨יג יָד֜וֹ “if he cannot afford” for the poorest.

2. He is not mentioned in our Mishnah text, but Mishnah 8 states that the High Priest is exempt according to everybody; only for the king does R. Aqiba disagree; Babli 9a. According to Tosephta 1:10, the king is exempted only for disregarding a request for testimony and the High Priest for violations of impurity (since his diadem is a permanent atonement for imperfect sacrifices, Ex. 28:38.)
The High Priest is required (Lev. 21:10) to be the richest priest; if he is not, the other priests have to make him so. R. Joseph David Sinzheim (Yad David on Horaiot) notes that the High Priest had the choice always to officiate at the burning of incense. Any other priest was given only a once in a lifetime occasion for this (Mishnah Yoma 2:4) since presenting the incense made the presenter rich (explicit in the Babli, implicit in the Yerushalmi, Yoma Halakhah 2:4, 40a 12). The king naturally has taxing powers.
Since king and High Priest are never able to bring a sacrifice according to the rules of the poor (Lev. 5:7–10) or the very poor (vv. 11–13), they are prohibited from ever bringing a sacrifice depending on the offerer’s wealth.

3. Text of B. It seems that this text presupposes a Mishnah mentioning only the Anointed; no such Mishnah is known.

4. Lev. 5:5.

5. Since the king is exempt from testimony and the High Priest for violations of impurity (Note 84), neither of them is qualified to bring a sacrifice for all cases enumerated in vv. 1–4; they are not under the rules of vv. 6–7.

6. The text in brackets, from B, is the only one making sense; the text of the ms., in parentheses, seems to be a scribal error.

7. Since the verse quoted at the start of the Halakhah refers to the poor sufferer healed from skin disease. But there is no verse requiring that the sufferer from skin disease be able to bring all possible sacrifices; the question does not deserve an answer.

8. Since a woman cannot be a formal witness in court, she cannot be the subject of an imprecation forcing here to testify. But the question is moot since women after childbirth are ordered in Lev. 12:6–8 to bring a sacrifice after being impure.

9. Lev. 6:13, the daily flour offering of the High Priest, identical in quantity to the variable sacrifice of the very poor. Babli 9a.

10. This is the correct attribution, against the text of B.

1. The fact that he does not judge is irrelevant for our topic (and certainly not true for Davidic kings.)