This does not mean that they were the sons of prophets, but rather, that they were a group of prophets. See how you translated this phrase in [2 Kings 2:3](./03.md). Alternate translation: "the group of prophets" (See: [[rc://en/ta/man/translate/figs-idiom]])
Here Elijah's "spirit" refers to his spiritual power. This speaks of Elisha having this spiritual power as if it were something that physically rested upon him. Alternate translation: "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]] and [[rc://en/ta/man/translate/figs-metaphor]])