The words "prayers" and "requests" mean basically the same thing and emphasize that the person is sincere as he makes his requests. (See: [[rc://en/ta/man/translate/figs-doublet]])
Here "plague" is a metaphor for sin, and sin and sorrow are spoken of as being in people's hearts. Alternate translation: "knowing the sin and sorrow in his own heart" (See: [[rc://en/ta/man/translate/figs-metaphor]])
This was a way of showing that they were praying to the God of the temple. See how you translated "spread out his hands" in [2 Chronicles 6:12](./12.md). (See: [[rc://en/ta/man/translate/translate-symaction]])