1)
Why did the water go around the Mizbe'ach?
1.
Radak: They poured (12 barrels) on the Olah and wood, which were in the middle of the Mizbe'ach. (It spilled over on all sides.)
2)
Who filled the trench with water?
1.
Rashi citing Eliyahu Rabah 17: Elisha (a Talmid of Eliyahu) poured water on Eliyahu's hands, and his fingers became like springs, and the trench was filled. "Po Elisha ben Shafat Asher Yatzak Mayim Al Yedei Eliyahu" (Melachim II, 3:11) - and a miracle was done via his hands, he (Elisha) is proper that a miracle be done via his hands.
2.
Radak #1: Eliyahu commanded that they fill it.
3.
Radak #2: Eliyahu himself filled it. This was in addition to the 12 barrels.