Above, Yaakov himself referred to Hashem as "Pachad Yitzchak" (31:42); why here does he refer to Him as "Elokei Yitzchak"? And why does he repeat the word "Hashem"?
Rashi: Yaakov was referring here to two promises that Hashem made to him - one, when he left his father in Be'er-Sheva on his way to Charan, where Hashem, referring to Himself as "Hashem, the G-d of Avraham your father and the G-d of Yitzchak" (28:13), promised to protect him wherever he went; the other, just before he left Charan, where, referred to by the Name "Hashem," He ordered him to return home and promised to accompany him (to protect him) (31:3). In the current Pasuk, Yaakov is evoking both of these promises - the first half of the Pasuk refers to the first promise (which partially quotes the words of Hashem himself - hence his use of the words "Elokei... Yitzchak"); 1 the second half, to the second promise, where Hashem mentioned only the Name "Hashem").
Hadar Zekenim (to 32:8), Da'as Zekenim (to 32:8): Yaakov thought that Yitzchak had died. Refer to 32:8:4:4.
Seeing as Yaakov's Tefilah begins only in the next Pasuk, what is the significance of this Pasuk?
Seforno: He began his Tefilah with words of praise 1 and Zechus Avos, just as the Anshei Keneses ha'Gedolah introduced into the Amidah.
Malbim: He explains why he should not be afraid. He should rely on his fathers' merits, and Hashem's promise. Only one who relies on his own merits must be concerned lest he sinned (and no longer deserves what he needs).
Ha'amek Davar: Avodah Zarah 7b says that one should do so. Avraham did not when he prayed for Sedom, for he was amidst a fixed prayer. Yaakov had already prayed Minchah, and now had a new need to pray.
Why did Yaakov pray only after he had divided the camp into two and not before?
Oznayim la'Torah (to 32:9): Because he was afraid following the news of his messengers, and was not able to concentrate fully until he began to make preparations for the forthcoming encounter and his fear abated.
Hashem said "v'Ehyeh Imach" (31:3); why did Yaakov change this phrase in his prayer to "v'Eitivah Imach"?
Oznayim la'Torah: If Hashem is with a person, that is the best thing that can happen to him.
Ha'amek Davar: "V'Ehyeh Imach" implies protection, but perhaps it is only for Yaakov, and not for his wives. Yaakov said that he understood that it is even for his wives, for Avraham's Berachah already guarantees that his seed will not be wiped out.
Why did he mention Elokei Avraham and Elokei Yitzchak?
Ha'amek Davar: Elokei Avraham hints to protection. Yaakov was concerned only for his [flock], slaves and wives, which are a person's income; this is the Midah of [the Berachah of] Yitzchak.
QUESTIONS ON RASHI
Rashi writes: "You promised me... in the house of Lavan, 'Return to the land of your fathers and to your birth place, and I shall be with you' (31:3)." But Rashi (loc. cit.) interprets that verse as a general promise for Hashra'as ha'Shechinah, not as a promise for protection?
Gur Aryeh: Nevertheless, we may derive that once Yaakov would leave Lavan's house, Hashem assured Yaakov to be with him in all ways. Also refer to 31:3:1.2:1.