The words "prayer" and "humble requests" mean basically the same thing and emphasize that the person is sincere as he makes his request. See how you translated similar words in [1 Kings 8:28](../08/28.md). Alternate translation: "requests" (See: [[rc://en/ta/man/jit/figs-doublet]])
Possible meanings are 1) The person's sin is spoken of as if it were a plague. Alternate translation: "knowing the sin in his own heart" or 2) The "plague" is a metonym for the sins that the disasters are a punishment for. Alternate translation: "knowing in his heart that the plague is the result of his own sin" (See: [[rc://en/ta/man/jit/figs-metaphor]] and [[rc://en/ta/man/jit/figs-metonymy]])