Why does it mention that David dwelled in his house?
'Rashi', Rashi (from Sanhedrin 20b): The Aron was in a tent (6:17). He said, Hashem fulfilled "v'Heni'ach Lachem mi'Kol Oyveichem." We must fulfill the next verse - "ha'Makom Asher Yivchar Hashem" (Devarim 12:10, 11) - now we should build the Beis ha'Mikdash!
Malbim (Shmuel II, 7:1): One condition for building the Beis ha'Mikdash is that we have a king. Since Chiram build a house for David, this showed that Hashem made him king over Yisrael, like I explained (refer to Shmuel II, 5:11:1:1).
Why did David say so to Nasan?
Radak, Malbim (both on Shmuel II, 7:2): Nasan should ask Hashem [whether or not] to build the Beis ha'Mikdash, and [if yes,] where 1 to build it.
When David fled Sha'ul, he and Shmuel derived that the Beis ha'Mikdash will be in Yerushalayim (Zevachim 54b, based on Shmuel I, 19:18)! Perhaps he asked where exactly in Yerushalayim. (PF)
What is "Beis Arazim"?
Radak (Shmuel II, 7:2, citing Targum Yonasan): It is a house covered with cedar wood.
Was David concerned only for the Aron?
Radak (Shmuel II, 7:2): He was concerned also for the other Aron, Mizbe'ach and Klei ha'Mishkan in Giv'on. All were under a curtain! He mentioned the Aron, for he spread the curtain for it, and it is most honored of all Klei ha'Mishkan.
