What did Yisro hear that aroused him to come out to the desert?
Rashi: He heard about Keri'as Yam-Suf and Milchemes Amalek. 1
Ramban: He heard about Milchemes Amalek - which the Torah just described. Refer to 18:1:1:1*.
Tosfos ha'Shalem (1): Before Milchemes Amalek, Hashem showed His power only in the water
Ramban (in Shemos, 2:16): His name was Yeser or Yisro 4 , only when he converted, he adopted the name Chovav 5 , and when the Torah writes (in Shemos, 2:18) "and they (the daughters of Yisro) came to Re'u'el their father, it means their grandfather. 6
Pane'ach Raza, Moshav Zekenim citing Sefer ha'Gan: He had an eighth name
Why does the Torah here refer specifically to Yisro as 'the father-in-law of Moshe' whereas in Shemos (4:18) it says that Moshe returned to 'Yeser his father-in-law' (without mentioning Moshe's name)?
Rashi: Because, whereas initially, Moshe was proud to be the son-in-law of Yisro (who had relinquished his belief in idolatry) now it was Yisro who was proud to be the father-in-law of Moshe 1 (who had since risen to greatness).
Moshav Zekenim (2): What is the source? "Chosen Moshe" is extra, to teach that he used to say 'I am his father-in-law!'
Why does the Torah see fit to mention Moshe individually?
What is the Pasuk referring to when it writes what Hashem did "on behalf of Moshe and Yisrael"?
Rashbam: It is referring to Pharaoh's inability to do him harm, and to how Hashem raised his prestige in the eyes of Pharaoh and his servants and to the miracles that Hashem performed with Yisrael through him.
Having said "all that Hashem did for Moshe and Yisrael", why does the Torah add "that Hashem took Yisrael out of Egypt?
Rashi: Because the miracle of Yetzi'as Mitzrayim was the greatest miracle of all.
Seforno: The Pasuk is saying that the above-mentioned miracles took place "when (not that) Hashem took Yisrael out of Egypt", 1 with reference to the ten plagues and the miracles that occurred then. 2
When exactly, did Yisro join Yisrael?
Whilst they were still in Refidim, and traveled with them from there to Har Sinai (See Ramban DH 've'ha'Karov Eilai' and Refer to 18:12:4:1*).
This is in accordance with the chronological order of the Pesukim. Further poof of this lies in the fact that Moshe only told Yisro about the various travails that they encountered on the journey and about Yetzi'as Mitzrayim - and said nothing about Matan Torah (See Ramban DH 'u'che'she'Amar').
See Ramban, who cites two opinions in Chazal (Mechilta and Zevachim, 116a), but begins by citing many reasons in support of this opinion.
According to the opinion that Yisro came after Matan Torah, why does the Pasuk mention his arrival before Matan Torah?
Ramban #1 (citing Ibn Ezra): To stress the difference between Amalek, who did us so much harm, for which we are obligated to pay him back, and Yisro, who did us a great favor, which we are obligated to acknowledge. 1
Rashbam (in Pasuk 13): The Torah inserts his arrival here in order not to break in the middle of the Parshah of Mitzvos (Rashbam).
Why does the Torah call Yisro "Kohen Midyan"? It is a disgrace to be the priest of idolatry!
Moshav Zekenim: It is because he reverted to his perverted ways. Refer to 18:2:1:2 and the note there.
One opinion in Shemos Rabah:Kohen is an officer, like "u'Vnei David Kohanim" (Shmuel 2:8:18).
Chizkuni: He was the great person of Midyan.
Ohr ha'Chayim: This is his praise
Why does it say 'what Elokim did to Moshe', and later it says 'Hashem'?
Moshav Zekenim: Initially, Midas ha'Din encountered Moshe [and wanted to kill him] when he returned to Egypt, for not circumcising his son. Hashem knew that Aharon will dissuade him from bringing his wife and sons to Egypt. 1 Had Moshe not circumcised his son, Bnei Yisrael would not heed his command that they circumcise.
I.e. Midas ha'Rachamim caused that Aharon met him only afterwards. (PF)
Rashi writes that Chever and Keini are both names of Yisro. "Chever ha'Keini Nifrad mi'Kayin bi'Bnei Chovav Chosen Moshe" (Shoftim 4:11) implies that Chever ha'Keini was Yisro's son!
Hadar Zekenim: Yisro's son was called the same name as his father.
Rashi writes that Yisro came before Matan Torah. Midrash Tanchuma says that because he did not suffer with Yisrael, he will not merit to be at Matan Torah!
Rosh (4): Moshe sent Yisro away before Matan Torah. Moshe was judging Yisrael (verse 13) about Mitzvos that they received at Marah, which included monetary laws. "Navol Tibol Gam Atah" includes Aharon and Chur, for Chur was killed only after [the Egel after] Matan Torah.
How can some say that Yisro was not at Matan Torah? It says "Tir'asim Shim'asim
Rosh (4): Perhaps Yisro's sons were exiled in Egypt and suffered [and merited to be at Matan Torah]. 1
Rosh: A support is "va'Yelech Lo El Artzo" (verse 27), and Rashi writes that that he went to convert his family. Where do we find that those converts came with Yisrael? Rather, we must say like I explained.