What are the connotations of the words "Tifk'du osam"?
Ramban: It means 'Remember and take note of them!' 1 In other words, Moshe was not just commanded to count Yisrael but to know their numbers by accepting their half-Shekalim as an atonement, so that they should not be subject to a plague that ensues when Yisrael are counted S'tam. 2
Targum Onkelos and Targum Yonasan: It means simply, 'You shall count them!'
Ramban: It is a Lashon of 'Hashgachah' (supervision), and is similar to the Pasuk in Bereishis 21:1 "va'Hashem Pakad es Sarah'.
Why does the Torah insert "Kol Yotzei Tzava" here?
Rashi: To teach us that a man under the age of 20 cannot be conscripted. 1
Ramban, Moshav Zekenim: Perhaps this is because it is only when a man turns 20 that he is strong enough to serve in the army, as the Mishnah states in Avos 'ben Esrim Lirdof'.
Ramban: And the Torah adds "l'Tziv'osam, because each tribe comprised large hosts.
Why is Aharon mentioned here, but not in the census at the beginning of Ki Sisa?
Ba'al ha'Turim: Because the census in Ki Sisa was instituted as a result of the Eigel, 1 for which Aharon was considered responsible, therefore it was inappropriate for him to have a hand in the counting.
To ascertain how many remained alive after the plague (Rashi on Pasuk 1).
Why were they counted from the age of 20?
Refer to 1:3:2:1 and the note there.
Moshav Zekenim: One who is 20 has many Mitzvos