What is the significance of Bnei Ches calling Avraham a prince of G-d?
Rashi (in Yehoshua, 14:15): As a reward for calling Avraham "Nesi Elokim', they merited forty years of peace whilst Hashem kept Yisrael in the desert.
Rashbam and Seforno: They were saying that since they considered him a 'prince of G-d', 1 he could bury his dead in the location where they buried the princes (or wherever he wished) 2 and did not need to wait till he purchased a burial plot. 3
Ramban: You are not like a Ger or Toshav. Hashem made you king over us! You may have any cemetery you want, unlike our custom (refer to 23:4:1:1*).
Malbim (5): The custom was, only esteemed residents could have a family burial site, like the Ramban 4 says. They stressed, we esteem you greatly
Rashi also writes in Shabbos, 105a that, based on this Pasuk, the Gemara learns that Hashem appointed Avraham king of the nations
Why did they say "Shema'enu"?
Ohr ha'Chayim: You want to bury your dead promptly. You have no need to delay! You may pick any place, and you need not pay its value!
Why did they say that no one will withhold his grave from Avraham?
Malbim (5): They said, we will not break our custom, that only residents may have a family burial site. You may bury Sarah anywhere in the communal cemetery. Or, you may buy an individual grave; no one will deny you even the grave designated for himself!
Ha'Emek Davar: It is what one designated for himself at the head of the site.