Audio of Lavi on Parshat Lech Lecha: Lech Lcha (yutorah.org)
The משך חכמה explains the words of ״אל הארץ אשר אראך״ as meaning that when אברהם gets to the land then ה׳ will show him off to everyone there.
The שער בת רבים explains that it specifies that אברהם took all his stuff because אברהם had such אמונה that he was going to stay there for good that he didn’t just look at his journey like someone who is checking out another town or community. Similarly, Rav Moshe says that אברהם didn’t even question ה׳ as to why he had to go to somewhere in order to receive the ברכה. We see that we should follow the מצוות just because ה׳ said so. And this is why the ברכה is called מגן אברהם. Another similar idea: the אור החיים says that אברהם went right when ה׳ commanded, and that’s what it means that he went ״כאשר דבר ה׳״.
The גר״א explains that the reason אברהם didn’t do ברית מילה until ה׳ commanded him even though he kept the whole תורה was because that was one מצוה that once אברהם he wouldn’t be able to do it again if ה׳ were to command it.
The תורה לדעת says that מלכי צדק gave אברהם bread and wine after the battle because you might have thought that אברהם went down in רוחניות, so bread and wine are the two items who have their ברכה raised (העץ to הגפן and מזונות to המוציא) showing us that אברהם also went up.
Rav Moshe explain that even though normally a ברית is a big שמחה for a person the reason it was a נסיון for אברהם was because his task was to be מקרב and it might be harder if he is different than everyone around him.
The מדרש says that the words יהא ברכה can be read as יהא בריכה, that he should be a pool/מקוה that just like a מקוה purifies people, so too אברהם purified people by being מקרב them. The אבני נזר explains further that the same way a מקוה purifies people but it itself doesn’t get damaged, so too when doing קירוב one shouldn’t get affected.
The כתב סופר asks, why didn’t אברהם stay in fancier hotels now that he had a lot of money from פרעה? He answers that אברהם didn’t let the money get to his head. However, the רל”ג answers that אברהם stayed there to be מכיר טוב that they let him stay in their hotel when he didn’t have any money, so now when he was rich he still stayed there.