Is second hand smoke dangerous for someone who is recovering from a pulmonary embolism?

Yes. Second hand smoke is dangerous for everyone, not just those recovering from pulmonary embolism. However, there can be diminished lung capacity after an embolism and impaired o2 transport so why take the chance?
Yes. This person has decreased lung capacity but in general second hand smoke is always dangerous.
Not particularly. Second hand smoke exposure is ill advised for everyone, but the risk is small and is highest for prolonged exposure over time.