Essence of Yitro: First, the gematria קטן of יתרו is 13, so he became a גר because he heard of the יג מידות הרחמים that כלל ישראל has. Second, Rav Moshe Tuvia Leif explains that יתרו first of heard of קריעת ים סוף and then how even with that עמלק still attacked the Jews, so he thought that he needed to do something because otherwise maybe he would become like עמלק. Third, one of the Slonim Rebbe said that יתרו only went to בנ״י after he heard about עמלק because once he saw that it was possible for people not to recognize ה׳ even after the miracles of מצרים he didn’t want to fall prey to that so he quickly went to בנ״י. Fourth, Rav Moshe Wolfson gave a different פשט. He quotes the באר מים חיים who brings a מדרש that ה׳ split the sea for דתן ואבירם. Further, the victory over עמלק happened even though שבט דן had עבודה זרה. We see from both of these incidents that ה׳ protects Jews even if they sin. So יתרו said that he wants to convert so that ה׳ will always protect him. Fifth, the תפארת שלמה explains that we praise יתרו for being the first person to say ברוך ה׳ even though בנ״י said אז ישיר because יתרו was the first person to give thanks to ה׳ for saving someone else. Sixth, the אמרי חן says that יתרו first said ״אשר הציל אתכם״ and then said ״אשר הציל את העם״ because first he was thanking ה׳ for savingמשה and אהרון specifically from פרעה and then he was thanking ה׳ for saving כלל ישראל.
The רל״ג explains that the פסוק says how משה thanked ה׳ for saving him from Egypt and from פרעה because Egypt represents the spiritual danger that they were saved from and פרעה represents the physical danger.
Thoughts on the Aseret Hadibrot/Har Sinai: First, Rav Ari Marcus explains that they blew the shofar at הר סיני was to show every Jew that they are free, the same way it is blown on יובל so that the slaves go free because אין לו בן חורין אלא מי שעוסק בתורה. Second, the רל״ג explains that seeing the voices means that they saw the תורה right in front of them. Third, Rabbi Gluck explains that it says that your animal should rest on שבת before saying that a גר should rest because when the non-Jews see even our animal resting they will want to become Jews. Fourth, the רבינו בחיי explains that it says ״וכל אשר לריעך״ after mentioning things not to be jealous of because the תורה is telling us that if you want some of what he has then you take כל, all of it, even the bad stuff that you don’t see. Fifth, Rav Moshe explains that the reason why ה׳ made it that we saw the thunder was to teach us that we can’t just listen or speak תורה, we need live it so intensely that it is as if it is tangible. Sixth, Rav Yitzchak Cairo says that the מדה כנגד מדה in getting a long life for respecting your parents is that since you will live to be old people will respect you the same way you respected your parents. Seventh, the Kotzker Rebbe says that the פסוק says that the nation was shaking and then they stood from afar. This teaches us that even though someone might be externally shaking and shuckling he could still be far away from ה׳. Eighth, Rav Binyomin Jacobs said that the reason we need הר כגגית is because sometimes we need to be forced to learn because it is hard. The רל״ג said another פשט. A barrel is empty. So ה׳ was saying that the only way to fill it up is through living a life of תורה. This explains why ה׳ had to specifically put the mountain over their head instead of just putting a real barrel. ה׳ was also teaching us that even if we learn we could still be like an empty barrel, so instead we need to live it. Ninth, Rav Binyomin Jacobs says that איש אחד בלב אחד means that only way we can become one person and united is through doing the will of ה׳.
Rav Yehuda Goldschmidt quoting the Maharil Diskin who explains that משה didn’t want to name his child אליעזר when he was still in the land of יתרו because the meaning behind the name is that he was saved from פרעה, so יתרו would think that משה is scared of the leaders of lands, so instead משה named him אליעזר when they were in the inn on the way.
The גמ׳ in קידושין says that even when we do עבירות we are still the kids of ה׳. We also know that על כנפי נשרים אביא אלי. The חתם סופר based on Rav Dovid Goldwasser explains that eagles are the most טמא birds, so we learn that even if we are like eagles and have done so many עבירות, we will still be brought to ה׳.
Rav Moshe explains that we say גרשום before אליעזר because משה remained a גר in מדין, represented by the name גרשום, and didn’t assimilate he was then able to say ״אליעזר״ that ה׳ saved me.
The פסוק says ״לא תעלה במעלות על מזבחי״. The חפץ חיים says that it means that a כהן shouldn’t raise himself up because he can bring קרבנות because it wasn’t because he did anything special to deserve it.