Why did R. Elazar not say, 'From here we learn that one should not refuse a great person and one should refuse a small person'; which would better fit the order of the Pesukim?

Ben Yehoyada: The Pasuk 'we will do so, as you have spoken' alone does not necessarily indicate that one may not refuse a great person, as it could simply reflect their humility. However, when they later refused Lot's invitation, it shows that one does refuse a small person and the reason that they did not refuse Avraham is because it is not permitted. If humility were the sole reason for their acceptance, they would have also accepted Lot's invitation. So R. Elazar first discussed a small person, as their behavior with Lot explains the reasoning behind their earlier behavior with Avraham.

Ben Yehoyada (Answer #2): Although the Pasuk about Lot is a clear proof, the Pasuk about Avraham is not so clear. One could have said that they had originally refused him, but the Pasuk wrote the conversation in a brief way. Therefore, R. Elazar mentioned the proof from Lot (i.e. the small person) first.

Why is the word 'Kantri' written in the singular, when there were 400?

Toras Chaim: Usually, when someone is accepting a large number of coins, he will not be particular if a few of them are not perfect. Here, Efron was particular that every single coin of the 400 was perfect.

Rashi explains that Avraham asked for fine flour and Sarah provided regular flour. However, there are some texts that say the opposite, that Avraham asked for regular flour and Sarah provided fine flour. How then, does this show that a woman has a more begrudging eye on guests than a man?

Ahavas Shalom (Rav Menachem Mendel of Kosov, Parshas Vayeira) The higher the standard of hospitality at the beginning, the more likely it is that the standards will decrease with time. It is also less likely that they will want to invite more guests in the future.

Nechamas Yehuda (Rav Yisrael Malin, End of Drush 5 L'Shabbos haGadol): Rashi (Pasuk 10, dh 'Kaeis') cites the Midrash, that the angels' visit was on the Yom Tov of Pesach. The Gemara (Pesachim 40a) teaches that a pious person should not 'Yiltos' - soak grain (out of concern that it will become Chametz). The Gemara also implies that the word 'Soles' (which we have translated earlier as fine flour) actually means soaked grain (as 'Yiltos and 'Soles' come from the same root word.) If so, Avraham wanted to give them regular flour ('Kemach') that was not ground from soaked grains, as he felt that the guests were pious people. Sarah did not assume that, so she would have given them 'Kemach Soles' - even flour from soaked grains. Thus, the Gemara's statement, that a woman has a more begrudging eye on guests than a man, refers to the lesser esteem in which a woman holds the guests.

Shaar Bas Rabim (Parshas Vayeira): Sarah had worked on herself so much, that she did not have this trait. This was so outstanding and unusual that the Torah emphasised it by relating that she said fine flour, since all other women have a more begrudging eye on guests than a man.

Beis Yisrael (Rav Yisrael Benvenisti, Drush 48): The implication of the Pasuk is not this way. Rather, Avraham was speaking and he first asked for flour and then for fine flour. Since a woman has a more begrudging eye on guests than a man, Avraham first asked for something smaller (i.e. of lower quality) and then followed up by asking for something bigger.

Ein Eliyahu: Since women have a more begrudging eye on guests than men, Avraham only asked Sarah for regular flour and as he assumed that she would not want to use fine flour. But Sarah replied that she would prepare fine flour, as she was especially righteous and did not have the same attitude as other women.

How does this fit with Shmuel's statement in Kidushin 70a-b that prohibits sending a woman greetings, even through her husband?

Tosfos (Kidushin 70b): The Gemara here is permitting asking a husband about the welfare of his wife. Shmuel was prohibiting sending a woman greetings via her husband.

How do Chazal say that 'Hashem changed her words', when Sarah did in fact say that she was old?

Ramban, Rashbam, Ibn Ezra on the Pasuk: She had also said that 'My master (Avraham) is old', which was left out by Hash-m. This is also considered to be a change.

How could the Gemara say that there was no old age until Avraham prayed for it? There are many Pesukim earlier in the Torah that mention old age?

Maharsha: Avraham prayed that old people should be recognisably old, through their hair and beard turning white.

Why did the Gemara quote the Pasuk in Parshas Chayei Sarah of 'Avraham was old in age'? It could have used the Pasuk earlier in Parshas Vayeira (Bereishis 18:11), 'And Avraham and Sarah were old'?

Maharsha: The Pasuk of 'and Avraham was old in age' was at a time when Yitzchak had matured and now had a beard which caused people to be confused and mix the two up. It was then that Avraham prayed and Hash-m made him look old.

Ben Yehoyada: As long as it was only the household members of Avraham who lived in his home, they were familiar enough to be able to differentiate between Avraham and Yitzchak. But once it was time for Yitzchak to marry, there was now a concern that his new wife would not be able to discern the difference between them, which would be very problematic. Therefore, it was at the time when Yitzchak was ready for marriage that Avraham prayed and Hash-m changed his appearance.

How does the Pasuk about Yaakov Avinu show that he was the first person to suffer illness?

R' Yeshaya Pick: The word 'הנה' - 'behold' indicates something surprising and striking.

If there was no sickness until Yaakov, why does the Midrash say (Bereishis Rabah Parsha 59) that Avraham wrote over all of his possessions to Yitzchak in a Diatiki? (A Diatiki is a document written for someone who is dying.) If Avraham was healthy and died suddenly, why would he write such a document? The Midrash should have referred to it as a gift document?

Ein Eliyahu: When a person would write a Diatiki, it was out of concern that he would die, since it would come suddenly without illness.

If there was no sickness until Yaakov, how can the Gemara in Bava Basra 16b say that Avraham Avinu had a precious stone around his neck and any sick person who looked at it would be healed?

Tosfos (Bava Basra 16b dh She'kol): Before Yaakov there was no illness that came 'naturally'; all came from a wound.

Tosfos Answer #2 (R' Tam and Ri): Until Yakov, no one became weak, i.e. mortal illness. From then and onwards, there was mortal illness, and no one recovered until Elisha.

Why did Yaakov pray for illness rather than Avraham or Yitzchak?

Iyun Yaakov: Yaakov had been promised that none of his children would die in his lifetime (See Midrash Tanchuma Vayigash 9). Therefore, he did not rebuke them until the day of his death, so that they would be able to repent and would not die soon after him. And since he did not know when he would die, he would only be able to rebuke them if something would signal that he would soon die. He therefore prayed to be ill before he would die.

How does the Gemara say that until Elisha came, nobody ever became sick and then healed, if the Midrash (Bereishis Rabah 65:9) teaches that King Chizkiyahu (who lived later) brought 'becoming healed from a sickness' to the world?

Bayis HaGadol (Pirkei D'R. Eliezer Perek 52:8): Until Elisha, no person was ever sick and was healed. After him, people could become healed through natural healings. After King Chizkiyahu, he introduced healing through prayer. (It could be that it is for this reason that Chizkiyahu hid the 'Sefer Refu'os' - 'the Book of Healings; and showed that it is Hash-m who heals.)