When did this episode occur?
Radak: It was when Shlomo returned to Yerushalayim from Giv'on. From it was seen the Chachmah that Hashem gave to him (and that the dream was true - Malbim).
Why does it say "Tavonah" (future)?
Radak: It is as if it says Ba'u. With the word "Az", past often comes in future tense, e.g. "Az Yashir Moshe" (Shemos 15:1), "Az Yavdil Moshe" (Bamidbar 21:17), "Az Yedaber Yehoshua" (Yehoshua 10:12), "Az Yivneh Shlomo" (11:7).
What is the meaning of "Shtei Nashim Zonos"?
Rav, in Shochar Tov 72:2: They were Ruchos, and took the appearance of women. Kli Yakar - they were the [demons] 1 Lilis and Na'amah, the 'source' of all women who are Mezanah 2 .
Shmuel, in Shochar Tov 72:2: They were literally Zonos. Ralbag - they sold Mezonos (food). Alternatively, they were harlots 3 . (Refer to Yehoshua 2:1:4:1-2 and the notes there.) Kli Yakar citing Mahari - even though harlots are brazen (can lie with a straight face), Shlomo judged correctly.
R. Binyamin, in Shochar Tov 72:2: They were Yevamos 4 . Drashos Ri ibn Shu'iv (Mishpatim u'Shekalim), Kli Yakar - normally, a harlot [does not want to become pregnant; if she gives birth, she] kills her son. A Yevamah (her husband died without children) takes another's baby to fraudulently exempt herself from Yibum or Chalitzah 5 .
We find that demons can change their appearance to resemble people (Gitin 66a, 68b). (PF)
Kli Yakar, Etz Yosef (on Shir ha'Shirim Rabah 1:10): We learn from the word "Nashim" which is superfluous.
Maharzu (on Shir ha'Shirim Rabah 1:10): How else would women, living alone in a house without men, give birth?!
Yedei Moshe (on Shir ha'Shirim Rabah 1:10): This would not explain why one was so foolish to insist that they kill the baby that she initially claimed! (Perhaps she feared lest the baby die by itself within 30 days, like her own baby did (refer to 3:16:3:3**); she thought that if he is killed, we assume that he was viable - PF.) Rather, 'Yevamos' alludes to a daughter-in-law who fell to Yibum, and her mother-in-law; refer to 3:25:1:1.
Ri ibn Shu'iv: We must say that her baby died within 30 days. He was a Safek Nefel; he forbids Yibum, but she needs Chalitzah due to Safek. (Why must we say that both were Yevamos? Perhaps only the liar was a Yevamah, and the other woman, even if she was a harlot, wanted to keep her baby, even if she did not need him to exempt herself from Chalitzah! - PF)
