en_tn/2ki/02/15.md

bowed themselves to the ground before him

They are showing him deep respect and acknowledging him as their new leader.

The spirit of Elijah does rest on Elisha!

AT: "Elisha does have the same spiritual power that Elijah did!" or "The spiritual power Elijah had is now with Elisha!" (See: rc://en/ta/man/translate/figs-metonymy)

in case the Spirit of Yahweh has taken him up and thrown him onto some mountain or into some valley

The sons of the prophets did not know for sure if Yahweh had taken Elijah to heaven or to another place, like a mountain or valley.