1) Rashi tells us that Hashem brought the sun out in full force so that Avraham would not be troubled with the burden of entertaining guests while recovering from his bris milah. Avraham, however, would not be dissuaded from doing his usual hachnasas orchim and went out “’kchom hayom,” in the middle of the hot day, to look for guests. Since Avraham would not give up, Hashem sent him the three angels as guests.
The meforshei Rashi ask: why did Hashem have to summon angels to appear as guests? Why didn’t he just remove the heat wave and then the usual parade of guests would have arrived on their own?
I saw a great answer:once the sun was out in full force, the mitzvah that Avraham set out to do was the mitzvah of hachnasas orchim in the face of difficulty, with tremendous tircha and effort. Had Hashem just lowered the temperature and taken away the heat wave, the mitzvah would have been easier, but an easier mitzvah is a different mitzvah entirely -- it would no longer be the same kiyum Avraham set out to accomplish.
2) Chazal learn from the fact Avraham and Sarah were blessed with the birth of Yitzchak right after they davened for Avimelech that a person in need who davens on behalf of someone else will have their own needs taken care of by Hashem. It seems from this Chazal that there is a cause/effect at work -- Avraham and Sarah’s tefilos for Avimlech caused Yitzchak (indirectly) to be born. Yet we know from the opening of our parsha that Hashem had promised Avraham and Sarah that they would have a son and Hashem even specified the date on which he would be born. Yitzchak's birth doesn't seem to have anything to do with the tefilos for Avimelech?
The Ohr haChaim answers that even when Hashem makes a promise, it doesn’t mean the recipient is free to just sit back and relax and do nothing. Rewards and zechuyos have to be earned. What Hashem’s promise accomplished is that just at the right time for Yitzchak to be born, Avraham and Sarah were presented with the tremendous opportunity to daven on behalf of Avimelech and through that to be zocheh to the child that they wanted.
There is no such thing as a free gift. What Hashem gives for free is the opportunity to earn the rewards desired.