What is "Kol Cheftzah" that he gave to her?
Rashi: He taught to her (Radak - everything she asked in) Chachmah.
A comment in Rashi, based on the Ari Zal 1 : He had Bi'ah with her, and from this came Nebuchadnetzar 2 , who destroyed the Bayis that stood for 410 years in the portion of all 12 Shevatim 3 .
Malbim: It is things that she saw in the king's storehouse, and desired them.
Afarkasta d'Anya (4, Inyanim Shonim 384): A Bas Kol called Nebuchadnetzar 'Rasha ben Rasha' (Pesachim 94a)! (Perhaps this is due to his paternal lineage, which was not from Shlomo. - PF) Bris Olam (on Sefer Chasidim 1019) - she bore a daughter to Shlomo; Nebuchadnetzar descended from her. The final letters of "Cheftzah Asher Sha'alah" spell Harah (became pregnant). In Divrei ha'Yamim II, 9:12 it adds "va'Tahafoch", to hint that from Shlomo came the one to destroy the house that he built. Nebuchadnetzar was saved when Hashem killed out Sancheriv's camp, because he descended from Shlomo. (Sefer Chasidim said, because he would raise and aggrandize Daniel, Chananyah, Misha'el and Azaryah.)
This is like the opinion (Yuma 12a) that Yerushalayim not was given in the portion of any tribe; it belonged to all of them. Surely, he 'expounds' the Gematriya of Nebuchadnetzar (422=410+12). (PF)
What is "Milvad Asher Nasan Lah"?
Rashi: Gifts and delicacies found here that are not found elsewhere.
Radak: It is in addition to what he gave to her corresponding to what she gave to him. Malbim - this is like it says in Divrei ha'Yamim II, 9:12 "Milvad Asher Hevi'ah El ha'Melech."
Why does it say here "Milvad Asher Nasan Lah", and in Divrei ha'Yamim II, 9:12 "Milvad Asher Hevi'ah El ha'Melech"?
'Rashi' (Divrei ha'Yamim II, 9:12): In Divrei ha'Yamim it says so for the honor of Malchei Yehudah; it implies that she gave to him more than he gave to her. Refer to 10:13:2:1.
What is "k'Yad ha'Melech"?
Radak: In abundance.
Why does it say "va'Tefen va'Telech l'Artzah"?
Midrash ha'Gadol (Chayei Sarah 25:5-6): When Avraham sent away Bnei Keturah, he told them, go to the east, as long as Yitzchak is subjugated among the nations. When you hear that they dwell serenely, come to serve them, so you will merit the table of Mashi'ach. They dwelled in their places until Shlomo rose and Yisrael dwelled serenely, they thought that he is Mashi'ach. This is why Malkas Sheva came 1 . When she saw that he is not Mashi'ach, "va'Tahafoch" and they returned to their place. Taima d'Kra - it seems that the Midrash expounds va'Tahafoch. This is why it cites the verse in Divrei ha'Yamim, and not the verse in Melachim, which says va'Tefen. How did she know that he is not Mashi'ach? The verse says that she was quite impressed! We can say that it is because he had Bi'ah with her, like it says in Sefer Ben Sira (p. 46). This is why va'Tahafoch is written next to "he gave to her Kol Cheftzah" [from which we expound that he had Bi'ah with her].
Malbim: Do not think that she made a big journey to see different lands, and happened to come to Shlomo by the way. Her purpose was only to see Shlomo; she did not turn to any other place. After she enjoyed seeing him, she went straight home.
Perhaps the riddles were to test if he has Ru'ach ha'Kodesh; she had received that "va'Haricho b'Yir'as Hashem v'Lo l'Mar'eh Einav Yishpot" (Yeshayah 11:3) - Mashi'ach will be able to judge [via Ru'ach ha'Kodesh] without witnesses (Sanhedrin 93b). (PF)