Why did he put his mouth on his mouth
Radak #1: This is like I explained about Eliyahu (Melachim I, 17:21), to direct his Tefilah on the one for whom he prays. Similarly, "va'Ye'etar Yitzchak la'Shem l'Nochach Ishto" (Bereishis 25:21). I.e. she was opposite him when he prayed, so he would put his intent on her, for she was barren.
Radak #2: Perhaps he did so to breath on him and warm him with natural heat that comes from the face and flesh. Most miracles are somewhat via a worldly (natural) method. Malbim - warming him enables him to receive revival. A miracle does not take effect on void, only on what exists!
Malbim: He matched the mouths to breath from his Ru'ach into the boy. He matched the eyes to give influence of sensation and understanding sensation. He matched the hands for the natural Nefesh to be revealed on the entire body from his hands. This prepared the three parts of the Nefesh to receive life.
What is the meaning of "va'Yighar Alav"?
Rashi citing Targum Yonasan: It is an expression of weariness; we find like this in Sifri.
Rashi citing Menachem: He lied on him.
Radak: He fell and prostrated on him. This is like "va'Yighar Artzah" (Melachim I, 18:42).
Malbim: He lied on him with all his strength 1 .
I.e. all his weight was on the boy. (PF)
Before (and in verse 35), he is called Na'ar. Why is he called Yeled in this verse?
Malbim: He had a new Leidah (birth).
Elisha thought that the staff would revive him. Why did he need to lie on the boy?
Malbim (29): Elisha had thought that he merely fainted.