A few notes from a daily journal

Hello Rabbi Michi,
With your permission, I am compiling here some comments that occurred to me regarding the beginning of Tractate Sanhedrin (which I studied in part with the Rabbi's excellent pages on the Tractate, thank you very much). I would be grateful if the Rabbi could briefly address some of them, and I apologize in advance for the length (I tried to be as brief as I could) –

1. On page 8. The Gemara offers a series of explanations on how to present the disagreement between the Rabbis and the Sages regarding the one who brings out a bad name. How does the Rabbi understand the above explanations? What is the idea of ​​presenting a simple disagreement in a mishna in a very side-by-side case? Is this an okimat? If so, what do they come to teach us, according to the Rabbi's method that okimat comes to remove a side-by-side interferer? Is what the Sages and the Rabbis wanted to teach us actually some small law regarding the warning of a female companion, and chose to teach it in the vague language of "one who brings out a bad name in twenty-three" in the middle of a mishna that is not entirely concerned with side-by-side laws but with the principles of halakha?
2. On page 13: During the dispute between R.S. and R.I. regarding the ordination of elders over the bull of the public, R.I. proves that it is obligatory to demand the word "and they ordained" (which adds another 2 to the number of elders) with the excuse "If so, I will not and they ordained for the sermon to write, "The elders of the congregation shall lay their hands on the head of the bull." The sermon is seemingly strange – was it supposed to say in the verse "The elders of the congregation shall lay their hands on the head of the bull before G-d and slaughter the bull before G-d"? This is a wording that is not at all acceptable. I found a Malbim that explains it (although it is a bit wordy – I assume it was supposed to say "and they ordained the elders of the congregation"), I would be happy to hear if the rabbi has another explanation.
3. On page 15. In the study regarding the male quarter – the Gemara there performs a study in two stages, to the best of my understanding. First, we study the verse “everyone who lies with a beast” in the sense of “if it is not a matter” of lying down, and then there is a deduction between lying down and lying down – that is, is there a deduction here between the plain text and the sermon of the verse? Between the word that is actually written and the word that we preached in “if it is not a matter”? I heard an explanation according to which the deduction is between the verse in Leviticus (“a man who gives his bed”) and the verse in Exodus, but I remember hearing from a rabbi that the deduction must be in the same verse or in the same matter in the Torah (and certainly not between the Pentateuch). How to understand this study?
4. On page 16. The Gemara studies several matters of Midrash regarding "the whole great matter," and specifies the differences in wording between Yitro's words and Moshe's description of the performance. Does it make sense to be meticulous about the wording of a casual statement by Yitro? There is actually a study of a body of laws regarding several dayanim from a statement by Yitro. Could it be that Yitro said something in a certain wording, and when Moshe Rabbeinu wrote the Torah, he wrote a different wording so that something could be learned from it? If so, where does the line cross? Perhaps sayings of Aharon, the daughters of Zelophehad from which we learn things were not said at all and Moshe wrote from his own mind? It is difficult for me to accept the explanation of the study of laws that is not a commandment of God, especially when it comes to such a statement…
5. On page 17. In a Rabbi's commentary on the purification of the worm – I thought there was an interesting example of a commentary in which the explanation is not a column/row explanation but an explanation of the very basic assumption of the commentary (that there is a common characteristic that creates the severity in columns and rows). There is a commentary here as appears in the Torah (of one given thing) – a snake is at the level of death and impurity 2X and pure, a reptile that is at the level of death and impurity X is not a law that it should be pure? And the explanation is not something lighter than a reptile that is impure, but a thorn that is, let's say, at the level of 1.5X and impure – meaning that the very connection between the level of "death" and purity is negated. Does the Rabbi also understand the commentary this way?
6. On page 18. When the Gemara tries to understand whether a high priest is exiled, it cites the verse that one who does not have a settlement in a city of refuge will not exile – and brings as proof a second verse that assumes that a high priest is already in a city of refuge in exile (“he never leaves there” – meaning exiled there!). How can one learn from there at all?

Thank you very much in advance!