What is "Keren ha'Shemen"?
Rashi: It is Shemen ha'Mishchah that Moshe made.
From which Ohel did he take the Shemen ha'Mishchah?
Rashi: It was in front of the Aron (Yuma 52b), in Ir David.
Radak: It was in the Ohel Mo'ed. Even though it was in Giv'on, Tzadok went there or he sent a Shali'ach to get it. Even though it says (Yuma 52b) that it was in front of the Aron, that was when the Aron was in the Ohel Mo'ed. When they took the Aron out to the war with Pelishtim, they left the oil and the jar of manna in the Ohel Mo'ed. It is unreasonable that they would remove them before the Ohel Mo'ed was brought to Yerushalayim, especially if in Yerushalayim was only the Aron with the broken Luchos, but the Aron with the whole Luchos was in the Ohel Mo'ed!
Why was Shlomo anointed a second time (Divrei ha'Yamim I, 29:22)?
Radak: Now only people of Yerushalayim anointed him. Afterwards, all officers of Yisrael from all the Shevatim anointed him. Then they anointed also Tzadok to be Kohen Gadol, and they made a great Simchah and slaughtered many Korbanos.