1)
Regarding Elisha's other miracles. It does not say that he prayed. Why does it mention prayer only here?
1.
Malbim (34, citing Akeidas Yitzchak 73): The other miracles he did through his power of Nevu'ah. Techiyas ha'Mesim is not given to a Shali'ach; only Hashem does it. The Navi merely prepared the body to receive life, but did not return the Nefesh.
2.
Malbim #2, citing the Zohar: Only his mother was prepared for the birth, but not his father. Therefore, his Chiyus (life-force) was weak; it lacked male influence. Elisha put this male influence on him, and was Ma'atzil (gave a 'copy' of) his Chiyus on him. He prayed to bring a new Ru'ach for the boy.