1. Yes, it modifies the following verb. It's close to "moderately" but with a positive meaning - ほどよい is like "just right" (as in Goldilocks + porridge)
2. もう死にます is not "am I already dead" , and is not a question but a statement: "I am going to (soon) die". She does not at all look like she is going to die, but she still says "I am going to die."