Having instructed Avimelech to return Sarah, why did Hashem see fit to add the fact that he is a Navi?
Rashi: To reassure him that Avraham would know that he had not had relations with Sarah, and that a. Sarah would therefore not be rejected by him, and b. he would willingly Daven on his behalf.
Why does the verse connote that Avimelech will die if Avraham does not pray for him?
Sha'arei Teshuvah (R. Yonah) 1:44: If one pained another, Hashem does not pardon him until he asks forgiveness from the one that he pained.
Moshav Zekenim: Avimelech was Chayav Misah. Avraham's Tefilah would save him