Why did he want a Navi?
Malbim: (a) To pray to Hashem for water. (b) To tell them their way (what to do).
Why was Elisha with them?
Radak: He had a Nevu'ah to go with them, to show them this great miracle. Perhaps Melech Yisrael will repent from his evil way. They did not know that Elisha is with them; he went amidst the people.
Why did he mention that Elisha poured water on Eliyahu's hands?
Rashi citing Eliyahu Rabah 17: This was at the episode on Har ha'Karmel. Eliyahu's fingers became like springs, and the trench was filled. Therefore Elisha is proper that a miracle with water be done for us via him!
Radak (based on Brachos 7b): It means that he served him. It does not say that he learned from him. This teaches that serving [a Rebbi] is greater than learning from him 1 !
Radak citing a Midrash: Even if Eliyahu requested water 2 , he would give it to him.
Malbim: Through pouring water on Eliyahu's hands, rain came 3 . He is habituated to such miracles, to bring water to the thirsty!
This is unlike Eliyahu Rabah 17, which explains that he mentioned pouring water to show why it is proper that a miracle with water be done via Elisha (refer to 3:11:3:1)! (PF)
I.e. do not say that Elisha only served Eliyahu for major matters, and he would tell other Talmidim to do small matters for Eliyahu. (PF)