How can Avraham describe himself both as a Ger (a sojourner) and as a Toshav (a resident) at one and the same time?
Rashi, Ramban and Rashbam: What he was saying was that although initially, he arrived from another country as a Ger, he had now become a Toshav - which explained why he did not yet possess a burial-ground. 1
Rashi #2: If they would grant him his request, he would behave like a Ger; but if not, he would take it by force like a Toshav, seeing as Hakadosh-Baruch-Hu had given the land to his descendents.
Ohr ha'Chayim #1: The Ramban (Hilchos Zechiyah 3:11) writes that one may give a gift to a Ger Toshav, for it is a Mitzvah to sustain him. This is proper conduct; also Bnei Noach should do so (although Avraham wanted to pay for it).
Ohr ha'Chayim #2: Avraham did not want to call himself only a Toshav, for Tzadikim do not consider themselves fixed in this world.
Malbim: Avraham wanted a burial site for his entire family. A Ger would not request this, for he does not intend to remain. A Toshav would not need to request this, for he already has a field, from which he can designate part for a burial site. I am a Ger
The Ramban adds that permanent residents tended to own their own family burial plots, whereas sojourners buried their dead in a communal plot. Hence Avraham's statement, that, since he had now become a resident, he wanted to purchase his own family plot of land. Note: This will also explain Rashi's comment on the words "Achuzas Kever." (EC)
Did Avraham address all of the Bnei Ches, when requesting a plot of land for a burial ground?
Ha'Emek Davar (3): Initially he addressed only Bnei Ches, i.e. the family of Bnei Ches and the city leaders; Efron was among them. Later he spoke even in front of Am ha'Aretz, who were great in number.
Why did Avraham say "v'Ekberah Mesi mi'Lefanai" At that moment, Sarah was not lying in front of him!
B'rachos, 18a: This teaches us that an Aveil who is obligated to bury his deceased is Patur from all Mitzvos, even if the deceased is not actually lying in front of him
Rashi (in B'rachos, 17b): Who is Patur because his mind is busy with the Mitzvah of burying the deceased.
Initially, Avraham said "give to me." Why did he later pay an exorbitant price?
Rosh: He meant "give to me permission to make it a burial site." He never intended to receive a gift.