Why does the Torah juxtapose the Parshah of B'nos Mo'av to that of Bil'am?
Rashi: Because it was planned by him. 1
Ramban: Because after Bil'am told Balak that he cannot overcome Yisrael, but they will not destroy Mo'av until the end of days, Balak provided Yisrael with wine and enticed them to sin, pretending to be their good friends. 2
Refer to 24:14:2:1 & 24:25:1:1. Ramban: In fact, it was not so much an act perpetrated by the women of Mo'av as a plot - planned by Bil'am and carried out by the elders of Midyan, to make Yisrael sin, as the Pasuk specifically states later in Pasuk 18.
Why did the Torah call the place "Shitim"?
Rashi (like R. Eliezer in Sanhedrin 106a): Because that was the name of the place.
Targum Yonasan (like R. Yehoshua in Sanhedrin 106a): Because they indulged in foolish activity - 'Divrei Sh'tus.' 1
See Sifsei Chachamim.
What is the meaning of "va'Yachel ha'Am ... "?
Da'as Zekenim: The people became Chulin through Bil'am's counsel. This is why he is judged in boiling semen, Midah k'Neged Midah.
Perhaps "va'Yachel" means to begin, i.e. the Zenus began with Bnos Mo'av. Refer to 25:1:152:2-4.
What is the implication of "va'Yeshev"?
Da'as Zekenim: "Va'Yeshev" always implies punishment - e.g. the sale of Yosef, the death of Yakov
Here it says that the Zenus was with Bnos Mo'av. Mo'avi women are permitted to marry into Klal Yisrael (Yevamos 76b), and this was not given (in Devarim 23:5) as a reason to forbid the men (for sending their daughters)! Yisrael fought Midyan to avenge making them stumble in Zenus, but not Mo'av, and it says that Bnos Midyan caused Yisrael to sin through Bil'am's counsel (25:17, 18: 31:15, 16)!
Abarvenel (31:1) #1, Malbim #1: They were Bnos Midyan. They pretended to be Bnos Mo'av, for Mo'av had made Shalom with Yisrael (Abarvenel). 1
Abarvenel (31:1) #2: Initially, Yisrael sinned with Bnos Mo'av (Malbim #2, Kli Yakar 31:15 - Bnei Yisrael went to them to entice them). When Bnos Midyan heard, they came to seduce them and entice them to serve idolatry.
Alshich (26:1): Bnos Mo'av seduced the easiest targets (the lowest men), i.e. ha'Am. Bnos Midyan seduced the Tzadikim (called Yisrael). Tzur commanded his daughter Kozbi to seduce Moshe or Elazar (Sanhedrin 82a)!
Agra d'Kalah (Matos 31:15): Initially, Bnei Yisrael would not sin without reason. They had a tradition that the kingship of Yisrael will come from a spark of Kedushah from Mo'av, so there was a great Yetzer to entice them. Only after they sinned with a 'reason', they sinned absolutely with Bnos Midyan, without a reason.
Malbim (Bamidbar 25:2): They were Bnos Midyan. Bnos Mo'av (and Amon) were modest; they are not blamed for not greeting Bnos Yisrael with bread and water, for "the honor of a Bas Melech is (to stay) inside" (Yevamos 77a). Bnei Yisrael thought that they are Bnos Mo'av.
This was after Yisrael defeated Sichon and Og (22:2), which was after Mo'av refused to let Yisrael pdonkey through their land (Rashi 21:13; Shoftim 11:17). Did Midyan not have Shalom with Yisrael? Yisro was from Midyan! Shach (Pinchas) - perhaps they pretended, for Yisrael despised Midyan, a son of Keturah (a Pilegesh). Or, they would kill Bnos Midyan for disgracing their grandfather (Avraham). Ohr ha'Chayim (15)