Why does the Pasuk use the word "Libchem" and not "Levavchem"?
What did Avraham mean when he said "Ki al-Kein Avartem al Avd'chem"?
Rashi: He meant that, since they had come to his home, they should do him the honor of coming in to partake of a meal.
Ramban: Now that they were passing his abode, it was only correct that they break their journey and rest by him for a short while.
Targum Yonasan: Since they arrived at meal-time, it was a sure sign that they had to accept his invitation and come in for a meal before continuing on their way.
What is the significance of the angels' reply "Kein Ta'aseh Ka'asher Dibarta"?
Targum Yonasan: 'You spoke well! Do as you said!'
Ramban #1 (citing the Ibn Ezra) and Riva: Although Avraham initially mentioned only bread, they, in their modesty, answered that that was fine with them.
Ramban #2, Seforno and Hadar Zekenim: They meant that he should do as he said (to serve a meal and let them recline a little), but no more, since they were on an important mission and did not want to be delayed. 1
Riva: You will do so (eat), but not we [angels]
Why did the angels accept Avraham's offer immediately, but initially refuse that of Lot?
Rashi (later in Bereishis 19:2): We learn from here that one refuses a 'small person' but not an important one.
Seeing as Avraham intended to serve his guests a full meal, why did he initially offer them only bread?