The Ramban holds that Keturah was not Hagar. Why did he not go to Charan to find a wife, like he did for Yitzchak?
Ramban (Pasuk 6): Avraham was fussy only with regard to Yitzchak, who was destined to build Klal Yisrael. He was not adamant about his other children. 1
What is the significance of the fact that the Torah writes that Avraham married Keturah right after Yitzchak married Rivkah?
Bava Kama, 92b: This is the source for the saying 'Sixty-pains the tooth that is not eating suffers when it hears its fellow-tooth eating. 1
Torah Temimah (citing the Aruch): Which means that a person who hears his friend eating and he himself is not eating, suffers 60 pains.
Why does it say "va'Yosef", especially according to Rashi, that he remarried Hagar?
Malbim: The primary seed of Avraham is Yitzchak. His other children are a mere secondary addition.
Ha'Emek Davar: Avraham remarried in order to have more children 1
Ha'Emek Davar: Alternatively, he remarried because "it is not good for man to be alone" (2:18).
The Gemara says that one fulfills even Peru u'Rvu with such children. According to the opinion in Bava Basra 16b that Avraham did not have a daughter, we can say that he remarried to fulfill Peru u'Rvu!
QUESTIONS ON RASHI
Rashi writes that Avraham remarried Hagar. Why does the Torah call her Keturah?
Rashi#1: Because her deeds were beautiful like the Ketores. 1
Rashi #2: Because she 'tied up' 2 her womb from the time that she left Avraham (refusing to marry any other man).
Targum Yonasan: Because she was initially 'bound' to him.