Why does it mention that David dwelled in his house?
Malbim: 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 above (refer to 5:11:1:1).
Why does it mention that David had respite from all his enemies?
Rashi (from Sanhedrin 20b): He said, after "v'Heni'ach Lachem mi'Kol Oyveichem", it says "ha'Makom Asher Yivchar Hashem" (Devarim 12:10, 11) - now we should build the Beis ha'Mikdash!
Why does it say that David had respite from all his enemies? He fought wars after this!
Radak: Before this, enemies came to fight. After Hashem helped David defeat all his enemies, they feared him and did not come to him. He went to them, and took Gas from Pelishtim, which previously belonged to Yisrael, and fought with Aram, Edom and Amon, with a claim.
