What does the Pasuk mean when it writes that Avraham "took" Yishmael and the other men of his household?
Ohr Ha'Chayim: Bearing in mind that Yishmael was already 13, Avraham took him with words - he convinced him (and the other members of his household) verbally 1 that this was the right thing to do, because he wanted them to perform the Mitzvos of HaSh-m willingly, not by force.
What is the significance of the phrase "be'Etzem ha'Yom ha'Zeh"?
Rashi #1 and Seforno: Avraham performed the Mitzvah immediately, on the same day that he was instructed.
Rashi #2: He was not afraid of those 1 who would try to stop him from fulfilling HaSh-m's command. That is why the Torah adds that he performed the Mitzvah by day, 2 so that nobody would be able to subsequently claim that, had they known about it, they would not have let him do it.
Moshav Zekenim (to Bereishis 18:1): Even though he did other Mitzvos early, here he waited until midday, for publicity. 3
Why does the Torah see fit to add the words, "like HaSh-m spoke to him," which seem to add nothing to the context?
Ohr Ha'Chayim #1: It is telling us that speaking to them softly (refer to 17:23:1:1) was itself by Divine command.
Ohr Ha'Chayim #2: It teaches us that Avraham did not delay carrying out HaSh-m's command, thereby demonstrating his Midas ha'Zerizus (alacrity).
Ohr Ha'Chayim #3: The Pasuk is telling us that Avraham fulfilled the Halachah derived from Pasuk 17:13, that only someone who is himself circumcised may circumcise others. 1