1) Ch. 31, v. 3: "Heicholtzu" - Rashi says that although Moshe was aware of his imminent death after the completion of the war against Midyon, nevertheless, he proceeded with joy. How do we know this?
2) Ch. 31, v. 16: "Hein heinoh hoyu livnei Yisroel bidvar Bilom limsor maal" – Behold they were for the bnei Yisroel through the word of Bilom to commit a betrayal – Which word of Bilom caused them to betray Hashem?
3) Ch. 31, v. 23: Kashering the vessels captured in war - Why were these laws not taught earlier, in the wars against Sichon and Og?
4) Ch. 31, v. 28: "Echod nefesh meicha'meish mei'ose" – One soul of five-hundred – This was the ratio of the spoils given by those who were actually involved in the war who received half the spoils. Those who stayed home, who in total also received half the spoils gave one of fifty, "Umimachatzis bnei Yisroel tikach echod ochuz min hachamishim" (verse 30). What insights do you have for the 1/50th and 1/500th tithes?
5) Ch. 31, v. 49: "Avo'decho nossu es rosh anshei hamilchomoh ASHER B'YO'DEINU v'lo nifkad mi'menu ish" - The words "asher b'yo'deinu" seem superfluous.