What are the implications of "ve'Atah Sechezeh"?
Rashi: It means via Ru'ach ha'Kodesh.
Seforno: Yisro was telling Moshe that, although the adjudication could be performed by the judges,, choosing the judges is something that only he could perform.
What is the definition of "Anshei Chayil
Rashi: Men of wealth, who need not flatter (they do not need others' money), men of integrity, on whose word one can rely, and to whom one therefore listens and - who are impervious to threat.
Ramban #1, #2: They must be men who are capable of leading large groups of people or who are strong and competent 1 incorporating the other three Midos - men who are G-d-fearing, who love the truth and who detest extortion (dishonesty). 2
Rashbam: Men who are wealthy and powerful and who are not afraid of anybody, men of integrity and men who detest bribery and what is stolen. 3
Seforno: With four levels (incorporating "Yir'ei Elokim" and "Son'ei Batza") of judges, 4 litigants who were not satisfied with the first, would go to the second, from the second to the third and from the third to the fourth - with the result that very few litigants would need to come to Moshe, thereby lightening Moshe's burden. 5
See Ramban's elaborate definition of the word "Chayil".
And obviously, men who are wise and learned, which went without saying (Ramban).
In Pasuk 25, the Seforno translates "Anshei Chayil" as 'Charutzim' (knowledgeable and diligent).
Which, as the Torah indicates in the next Pasuk, was the main objective of Yisro's advice.
What is the meaning of "Son'ei Batza"?
Ramban #1 (citing R. Yehoshua in the Mechilta) and Targum Yonasan: They are loath to accept bribery. 3
Ramban #5: Refer to 18:21:2:2.
Ramban: This refers to property that is truly his, but others could take it in Din, i.e. he does not have a proof that he bought it. (Such a person hands it over voluntarily). The Mechilta implies unlike this. Moshav Zekenim, Rosh
Why does the Torah begin the numbers from the most and progresses downwards - officers of 1000 to officers of 10?
Rashi: Because as far as the number of officers is concerned, it begins from the least and progresses upwards - from 600 officers of 1000, up to 60,000 officers of 10. 1
See also Targum Yonasan on Pasuk 25 and Peirush Yonasan there.
It already says "Yir'ei Elokim." Surely they are truthful
Moshav Zekenim: They get the correct Halachah. Beis Shamai and Abaye were Yir'ei Elokim, but [usually] the Halachah does not follow them against Beis Hillel or Rava.
Rashi writes that there were 600 officers of 1000, 6000 officers of 100, 12,000 officers of 50. This adds to 18,600; less than 600,000 Yisraelim remained. Why were there 60,000 officers of 10?
Da'as Zekenim #1: First they appointed 60,000 officers of 10, and from the 60,000 they choose 12,000 officers of 50, and from them 6000 officers of 100, and from them 600 officers of 1000. 1 2., Hadar Zekenim #1, Riva: The judges were not among the count of 600,000, for they were above 60 years old (or from Shevet Levi - Moshav Zekenim citing R. Yeshayah). Da'as Zekenim #2
Da'as Zekenim, Riva: It says in Sanhedrin (18a) that there were 78,600 officers! This counts titles (i.e. a single judge can be counted up to four times, of he was a judge over 1000, 100, 50 and 10).