What is the significance of the phrase "Ki Am Kadosh Atah"?
Rashi (in Seifer ha'Pardes): 'If you will sanctify yourselves from all forms of desecration and filth, to be clean and pure before Hashem, He will choose you and your Tefilos
This explains why Avraham did not cry much over Sarah (as hinted by the small 'Kaf' in "ve'Livkosah" - in Chayei Sarah Bereishis, 23:2).
See Oznayim la'Torah. In any event, according to the commentaries, the very term "Kadosh" implies to eternity.
What is the corollary between "Ki Am Kadosh Atah ... : and "u'Vecha Bachar Hashem"?
Rashi #1: 'Because, due to your forefathers, you are already an Am Kadosh; moreover, Hashem chose you ... '.
Rashi #2 (in Seifer ha'Pardeis): 'If you will sanctify yourselves from all forms of defilement and filth, to be clean and pure before Hashem, (for that) He chose you and your prayers - because He is Holy and all His servants are holy.
Why does the Torah mention here the fact that Yisrael are an "Am Segulah" (a treasured or a beloved nation) from all the nations".
Seforno: Becaus it is due to the fact that they are an Am Segulah that Hashem forbade them - and not the Nochrim - to indulge in these practices.
What is the connection between this Parshah and the previous Pesukim?
Seforno: The difference between Beheimah Tehorah and Beheimah Teme'ah was already known in the time of No'ach, yet when Hashem permitted Noa'ch to eat meat, he did not draw a distinction between them as He is doing now with Yisrael.