What exactly, does the word "Elonei (Mamrei)" mean?
Targum Onkelus and Targum Yonasan: It means the plains of (Mamrei).
Rashi: It is the name of the plain belonging to Mamrei (Avraham's friend).
What is the significance of Avraham's friend 'Mamrei' and that the town Chevron?
Rashi (in the initial print): Avraham's friend was called 'Mamrei' because he rebelled against the idolatry that his contemporaries worshipped; whereas 'Chevron was so-called because he (Mamrei) attached himself to Hashem.
What is the significance of the fact that Avraham settled down in Kiryas Arba (in Chevron)?
Rashi (later Bereisis 21:34): This took place in the same year that he arrived from Charan. Until now, he had traveled from one place to another (including spending three months in Egypt), and this is the first time that he settled permanently in one place. He remained there until the overturning of Sedom twenty-five years later. 1
רש"י: ממרא - שם אדם: אולי זה שם מקום?
גור אריה: כבר כתוב שהמקום היה בחברון.
רש"י: ממרא - שם אדם: אולי "ממרא" הוא שם המישור?
גור אריה: שם המישור הוא אלוני [עי' רש"י לקמ' יד,ו].