Here David is referring to himself by his heart. Also, the word "fixed" means to trust completely. AT: "My heart is fixed on you, God" or "I am trusting completely in you, God" (See: [[rc://en/ta/man/translate/figs-synecdoche]] and [[rc://en/ta/man/translate/figs-idiom]])
Here David is represented by his "heart." David refers to himself as having the honor of praising God. AT: "You honor me by allowing me to sing praises to you" (See: [[rc://en/ta/man/translate/figs-synecdoche]])