1. A fancy answer to why the malach sent to save Lot visited Avraham first (see last post)is as follows: Lot was saved because he would give rise to Moav, leading to Rus, leading to David haMelech and the lineage of Moshiach. Even in David's lifetime, there was those who thought he should not even be accepted and allowed to marry into Klal Yisrael. After all, the Torah says with respect to an Amoni and Moavi, "lo yavo b'kahal Hashem." The counterview, which prevailed l'halacha, darshened the pasuk as applying to a Moavi -- but not a Moavis, which meant Rus was kosher. What is that derasha based on? The reason the Moavim were excluded is because, "asher lo kidmu eschem b'lechem..." that they did not come out and offer food and drink to Bnei Yisrael when they passed their territory. It is the job of the men, not the women, to go out and greet others, says the gemara, and so only the males are excluded from Klal Yisrael. The proof that this is correct comes from our parsha. When the angels come to Avraham tent, they ask, "Ayei Sarah ishtecha?" where is Sarah. Avraham was the one who greeted and served the guests; Sarah remained behind the scenes, demonstrating her tzeniyus. The malach sent to Sdom had to see this behavior to ratify the derasha that excluded Moavi women, allowing for the future hechsher of Rus and David, which justified Lot's being saved.
Last's posts answer was easier to explain : )
2. Rashi writes that Yishmael was arguing with Yitzchak over the right of inheritance, and therefore he and Hagar were expelled from Avraham's home. How old was Yishmael at this time? Remember, Yishmael was already 13 when Yitzchak was born, and if the events of the parsha are recorded in order, Yitzchak was already more than 2 years old, as they already had a party to celebrate his being weaned. Realistically, he must have been a few years older to understand yerushah. So was Yismael around 20? (The Midrash says he was 17). How can Rashi be correct, asks Ramban, when we read in the parsha that Hagar hoisted the sick Yishmael (called a 'yeled') on her shoulders? Could Hagar carry a 20 year old boy plus the provisions she had?
R' Shteinman answers that no matter how big Yishmael was, a mother always has the strength to bear the burden of carrying her child.
I don't know if it's a pshat answer (see Gur Aryeh and the meforshei Rashi who discuss the issue), but it's an answer that's true anyway.
3. Speaking of bearing burdens, there is a Tzeidah la'Derech that has a beautiful comment on the repetition of "vayeilchu sh'neihem yachdav" 22:6 and again in 22:8 in the akeidah. Since the Torah makes the point of saying it a second time, it means that the first time didn't work, that the were not walking in sync yet until the second time.
An elderly person and a young person usually do not walk at the same pace. Avraham was an old man; he would have walked more slowly than the younger Yitzchak. In 22:6 the Torah tells us that Avraham gave Yitzchak the burden of carrying the wood to slow him up so that they would walk together, the first "vayeilchi sh'neihem yachdav."
Apparently even with the wood on his back, Yiztchak was walking faster. The Torah then tells us that Yitzchak asked Avraham where the sheep for the korban is -- they have the wood, the knife, etc., but no animal? Avraham (22:8) cryptically answered that G-d will show them then sheep. Yitzchak at that moment understood exactly what was going to transpire, that he was the korban. Now, "vayeilchi sh'neihem yachdav." The burden of the wood was something he could carry and still outpace the gait of Avraham, but the psychological burden of the impending akeidah was enough to slow Yitzchak's gait to match that of his father.