What tent did David spread for the Aron?
Radak: He spread a curtain above.
When the Aron was in Beis Avinadav and in Beis Oved Edom it was in a house with a roof, and it does not mention a tent!
Radak: There, it was temporary. David knew that it will be in Yerushalayim permanently. There was a tradition that it is Ir ha'Kodesh, and the Beis ha'Mikdash will be built there. Even though David did not know the place of the Mikdash until he built the Mizbe'ach based on Gad ha'Navi, and fire descended from Shamayim, he did not want to house the Aron under a roofed house until then, rather, under a curtain, like it was before, in Giv'on 1 .
It was under a curtain also in Shilo (Zevachim 112b), and when it was in Gilgal and Nov (Radak Divrei ha'Yamim I, 17:5).
What was in this Aron?
Radak #1: Now that the Ohel Mo'ed was in Giv'on, and Mishkan, Aron with the two [whole] Luchos and Klei ha'Kodesh were under a curtain, also this Aron with the broken Luchos was put under a curtain [in Ir David].
Radak #2: This Aron held the whole Luchos. This is primary, like I explained above (Shmuel I, 4:4). This Aron was [later] brought into the Kodesh ha'Kodoshim in the Beis ha'Mikdash.
Radak #3: This Aron housed the second Luchos and the broken Luchos, according to an opinion in Bava Basra 14a.
Why did David not bring this Aron to Giv'on, where the Mishkan was?
Radak: He knew that the Mishkan would later come to Yerushalayim. He thought that it will be in his lifetime, for he will build the Beis ha'Mikdash. After bringing it, he asked Nasan ha'Navi if he may build the Beis ha'Mikdash, and Nasan agreed (on his own, without Nevu'ah), for he thought like David (7:2, 3).
Why did David himself offer the Korbanos?
Malbim: He was aroused to do so amidst Simchah of Mitzvah, to draw an influence of Hashem's desire.
