Why does it say that David ruled over all of Yisrael?
Radak (Shmuel II, 8:15): He won all the wars, and Beis Sha'ul was wiped out, so no one had any doubt about his kingship.
Why does it say that David did Mishpat and Tzedakah?
'Rashi': He refrained from going out to war, and sat and judged Yisrael righteously.
Rashi (Shmuel II, 8:15, from Sanhedrin 49a): Because David did Mishpat and Tzedakah, Yo'av succeeded in war (verse 16 hints to this). Yo'av enabled David to do Mishpat and Tzedakah. David judged, and Yo'av enforced his rulings. Also, because Yo'av engaged in wars, David was not distracted with them, and his heart was open to judge correctly.
Targum Yonasan (Shmuel II, 8:15): He did correct judgment and merit. Radak - he would judge the case between the litigants, and do Tzedakah when they needed. R. Yehudah (Devarim Rabah 5:3) - he vindicated the innocent and obligated the liable, and if the liable could not pay, David paid for him.
Kli Yakar (Shmuel II, 8:15, citing R. Nechemyah (Devarim Rabah 1 , Shoftim 3)): He was Matzdik (justified) the Gazlan's soul via removing the theft from his hand.
Malbim (Shmuel II, 8:15) : They requested two matters from the king (Shmuel I, 9:20) - "our king will judge us... and fight our wars." After David turned from war, he engaged in judging, and also did Tzedakah and Chesed to the poor.
Devarim Rabah (5:3, in the standard (Vilna) edition): He vindicated the innocent and obligated the liable ? this is Mishpat. It was Tzedakah to take the theft from the thief's hand.
