How did Belshatzar know that Daniel was interpreting the writing correctly and not just deceiving him?

Rav Saadia Gaon (Sefer Daniel): When others gave their interpretations, the writing remained on the wall. But when Daniel gave his, the writing immediately disappeared, showing that the Divine message had been truly understood.

Why specifically does the altar shed tears over divorcing one's first wife?

Toras Chaim: Adam and Chava were originally created as one body, back-to-back. Chazal tell us that they were formed from earth from the place where the Pasuk states (Shemos 20:20), "Make for me an earthen altar". Therefore, when a person divorces his first wife, he makes a type of blemish in the altar from which he was created.

Chasam Sofer (Shut Chasam Sofer 7:34): When a man divorces his first wife, it is considered the loss of his Zivug Rishon, which occurs because either he or she has spiritually declined through wrongdoing. Chazal teach (Bamidbar Rabbah 21:19) that no one ever went to sleep in Yerushalayim with an Aveirah in hand, as the daily Tamid offering would atone for the sins of all of Am Yisrael. However, this was only true if the individual had repented. Therefore, it must be that this person who is divorcing his wife did not properly repent and thus did not receive atonement. As a result, the altar "cries", as it was unable to fulfill its purpose of securing atonement for this individual.

Why is it as if the Beis haMikdash was destroyed in his days?

Ben Yehoyada: When the Mikdash was standing, all could recognize the strong relationship that Yisrael had with Hash-m., like the relationship between a husband and wife. (This is the central theme of Megillas Shir haShirim). But with the destruction of the Mikdash came a separation. This is like a wife who is widowed and is no longer in her husband's home.

What is the meaning of the phrases 'the world becomes dark for him' and 'his footsteps becoming shortened' and is there a connection between them?

Toras Chaim: The Gemara (Yevamos 63a) states that when a wife helps her husband, she ' lights up his eyes and stands him on his feet'. Both of these are therefore lacking when his wife passes away.

Maharsha: Since he must now take care of the home, he cannot travel far away to earn his living, so 'his footsteps become shortened'.

Ben Yehoyada: 'His world becomes dark for him' means that when his wife was alive, she managed the household, and he would only come home at night. But now that he must also take care of the home, he needs to be present during the day as well. In this sense, his daytime has become like his nighttime.

Korban Asher: The Gemara tells us (Berachos 43) that taking large strides damages the eyesight of a person. On the other hand, the Gemara in Yevamos 63 states that a wife 'enlightens the eyes' of her husband. Thus, as long as she is alive, he does not need to be so careful about taking large strides. But after she dies, he no longer has this protection, so he must be careful to take smaller steps.

Why will a man's advice fail him when his wife dies?

Ben Yehoyada, Ein Eliyahu: His wife advised him in various matters of the physical world, but he no longer has that.

Maharsha: If they merit it, when they are married, the Shechinah rests between them, and the advice of Hash-m is with them. When she dies, the Shechinah leaves that home.

What was so unique about the splitting of the sea and its comparison to pairing up marriage partners?

Maharal: Even though the plagues struck the Nile and land of Egypt, they do not compare to the Sea's splitting. The Nile is a specific river, but the sea, though composed of many parts, is collectively called "the sea," as in "to the gathering of waters He called seas." The sea is a unique creation, as it says: "The sea is His, for He made it." It stands alongside dry land and represents a basic element of nature. When Yisrael overcame the natural order of the sea and it split, it was a victory over the physical world and nature itself.

Chida (Pesach Einayim Sota 2a from Tosfos citing R' Tam): When the Gemara refers to a "first" and "second" marriage, it means that for both individuals, it is a second marriage - for example, a match between a widower and a widow. This is one reason why making matches is described as being as difficult as splitting the sea. Just as Hash-m had to orchestrate the downfall of the Egyptians in order to redeem Yisrael at the sea; so too, in the case of a second marriage, He may have brought about the passing of the original spouses in order to bring about this new marriage.

Rav Yisrael Reisman: Bnei Yisrael did not cross the Yam Suf from one side to the other, but entered and exited on the same side in a semi-circular path, allowing them to continue directly toward Eretz Yisrael. Therefore, each of the 12 tribes followed a different semi-circle, some shorter and easier, some longer and harder. This explains the Gemara that says finding a shidduch is like Kriyas Yam Suf: everyone's journey is different; some quick and smooth, others slow and challenging; but all are guided by Hash-m.

Arizal (from Zohar Parshas Lech Lecha), Yaavetz/ Be'er Sheva in Sota 2a: Zivug Rishon, which is announced before a person is born, corresponds to the original structure of the person's soul. Zivug Sheni, considered a more difficult match to make, refers to the person at the time they are ready to marry, after they have matured and based on the actions they have taken. These actions may have altered their original spiritual makeup, thereby changing who their appropriate match is.

Minchas Elazar (Intro to Shut Vol. 4): The Gemara's "first and second match" refers to two stages of matchmaking before marriage. The first match is the ideal soulmate, assigned by Hash-m based on foreseen good deeds. If the person sins, they may lose that match and receive a second, lesser one based on their actual behavior. This explains why matching is "as difficult as the splitting of the sea" - just as Hash-m saved Bnei Yisrael by considering only their future merits and not their sins, so too He assigns a soulmate based on the good He foresees.

Why was there no prohibition of Lashon Hara for Rav Yehuda to tell his son Rav Yitzchak that Rav Yehuda's wife (Rav Yitzchak's mother) was 'more bitter than death'?

Chafetz Chaim (Klal 1 Be'er Mayim Chaim 13): Two reasons combined to permit it - Rav Yitzchak already knew of her nature and Rav Yehuda did it for the purpose of explaining the Pasuk.

What is the meaning of 'a man dies only to his wife and a woman dies only to her husband'?

Iyun Yaakov: A man dies because of the sin of his wife - as we find that Elimelech died for the sin of his wife Naami leaving Eretz Yisrael. A wife dies because of the sin of her husband - as we find (Midrash Tanchuma Vayishlach 8) that Rachel died because her husband Yaakov delayed in fulfilling the vow that he made in Beis Kel (Bereishis 28:20-22).