Why did Hashem order Yisrael to be counted now?
Rashi #1: It can be compared to a shepherd, who after his flock was attacked by wolves, counted the sheep to see how many remained. 1
Rashi #2: When Yisrael left Egypt, they were handed over to Moshe with a census; now, when Moshe was about to die, he handed them back with a census.
Da'as Zekenim: This was to know who will fight the Cana'anim - in the imminent conquest of Cana'an. 2
Chizkuni (on Pasuk 2): "La'Eileh Techalek ha'Aretz" (Pasuk 53) teaches that it was for the distribution of Eretz Yisrael.
Alshich: It was in order that Hashem put his name on the families to testify about them (refer to 26:5:2:1).
Why is there a P'sik (a Parshah- break) in the middle of the Pasuk?
Riva and Moshav Zekenim #1: This hints that the previous Parshah (to fight Midyan) is out of place, since it was only told to Moshe in Parshas Matos -after the census. 1 And it is written here to teach us that, since B'nei Yisrael died on account of Midyan, they deserved to die. 2
Moshav Zekenim #2: It is to separate Yisrael from the punishment of the plague, and to teach us that there were not [significantly] less than the first count. 3
Targum Yonsan: Because the first part of the Pasuk refers (also) to the previous Pasuk - 'After the plague, where Yisrael were smitten, Hashem's Mercy welled on behalf of Yisrael' - to avenge what was done to them, since it is appropriate for those who caused them to fall to be smitten just as they were. 4
Moshav Zekenim: A support for this is the fact that "Tzaror" is written with a Kamatz. A command would have been written 'Titzror', or 'Tzeror' with a Sheva! Rather, in the future Yisrael will afflict them. (Another support lies in the word "Vay'hi Acharei ha'Mageifah" - which always implies a long time afterwards.
Riva and Moshav Zekenim #1: If even an animal through which a Yisrael sins (with bestiality, and he is killed), the animal is killed, all the more so Midyan!
Hadar Zekenim (on Pasuk 59): There were [a drop] fewer in this count, lest people say that a smaller amount could not have conquered Eretz Yisrael. We learn that Hashem has no constraint to save, through few or many. Only three hundred men went with Gid'on!
According to the explanation of the Na'ar Yonasan citing Midrashim and Oznayim la'Torah.