Shekalim 8:8 - Yoma 1:1

מחצי כבש ולמטה במערב – the Kohanim/priests who obtained the privilege by the arbitration regarding the limbs of the daily offering to bring them up would not bring them up all at one time, but would place them on the ramp and walk to the chamber of Hewn Stones (where the Sanhedrin sat) to recite the Shema and afterwards return and offer up the limbs on top of the Altar as it is taught [in our Mishnah] here, that they are placed on the lower half of he Altar-slope. For the ramp was thirty-two cubits long and from its half-way point downward, they would place them, and the width of ramp was sixteen cubits and on its lower half to the western side, they would place them (i.e., the limbs of the daily offering).

ושל ראשי חדשים – from it half-way point and upwards which is on the rim of the Altar that surrounds it and toward the east.

אינן נוהגים אלא בפני הבית – Shekalim because they are for the needs of a sacrifice, and since there is no sacrifice, there are no Shekalim. But regarding the First Fruits, as it is written (Exodus 23:19): “The choice first fruits of your soil you shall bring to the house of the LORD your God." At the time when you have a Temple, you have First Fruits; when you don’t have a Temple, you don’t have First Fruits.

אבל מעשר דגן וכו' נוהגים בפני הבית ולשא בפני הבית – for the Holiness of the Land [of Israel] is never invalidated. Therefore, it is necessary to separate out Terumot and Tithes and for the Tithe of Cattle, you must separate a tenth. But in Tractate Bekhorot (see Chapter 9, Mishnah 1), they stated that they invalidated the tithe of the cattle so that it should not come regarding it as a stumbling block/snare.

המקדיש שקלים ובכורים – which was not practiced other than when the Temple stood, but if one separated them when the Temple no long existed, they are sanctified.

בכורים אינן קדש – since it is explicitly written concerning them (Exodus 23:19): “you shall bring to the House of the LORD your God,” even if he had separated them post-facto, they are not holy and the name/title of Bikkurim/First Fruits does not take effect upon them because the Temple doesn’t exist. But Maimonides explains that one who sanctifies Shekalim and First Fruits for the upkeep and maintenance of the Temple that he already has, but according to his explanation, the reason for why, according to Rabbi Shimon that Shekalim are holy, and First Fruits is not holy is not clear. But the Halakha is according to Rabbi Shimon.

Seven days... We separate the High Priest. Since all the service of Yom Kippur is not kosher except through him [Yuma 32a and many other places], as it says in regard to Yom Kippur (Vaikra chapter 16) "And the Cohen ,who will be anointed with oil, will atone." [note of the translator: from this verse we see that only the anointed Cohen, i.e. High Priest can perform atonement service of Yom Kippur]. And this separation is learned out for us from what is written in regard to seven days of the dedication [of the Mishkan] (ibid. chapter 8) "And from the entrance of the Tent of Meeting don't go away for seven days", and after this it is written (ibid.) "Just like was done on this day commanded Hashem to do to atone for you", and the sages expound: [the phrase] "to do" this is doings of the cow [red heifer], [and the phrase] "to atone for you" this is doings of the Yom Kippur. Thus, the Cohen that burns the cow [red heifer] and the Cohen serving on Yom Kippur, both require separation from their houses for seven days just like were required Aharon and his sons during the seven days of dedication [of the Mishkan]. [note of the translator: thus, from the proximity of the two verses, the verse that talks about the seven days of separation during the dedication of the Mishkan and the verse that was expounded to mean "just like was done on this day, commended Hashem to do for the procedure of the Red heifer and the Yom Kippur service", the sages learn that the Cohen that does the burning of the red heifer and the High priest that serves on Yom Kippur should be separated from their houses similar to the seven day separation of the days of dedication of the Mishkan.]

ללשכת פלהדרין – the officers of the king are called Palhedrin/counselors, for since that the High Priests that existed in Second Temple times after Shimon HaTzaddik/the Righteous (see Mishnah Avot, Chapter 1, Mishnah 2) would give money in order to serve in the High Priesthood, and because they were wicked, they would not complete their years, and would be exchanged every twelve months like the officers of the king, who would exchange them every year, therefore, they call this apartment the apartment/cell of the counselors.

ומתקנין לו – They would invite another Kohen to become the High Priest in his place if a nocturnal pollution would occur to him or some other kind of defilement.

אם כן אין לדבר סוף – if so, that he would concerned for his death, and there would be no end to this, lest she (i.e., his wife) would also die, but for defilement that is frequent we are concerned, therefore we appoint for him another Kohen, for death is not frequent that he would die suddenly, we are not concerned, therefore, we do not appoint for him another wife. And the Halakha is according to the Sages.