With acute exposure. Someone allergic to cats who lives with cats will not likely have acute anaphylaxis but may have symptoms of chronic allergic rhinitis and asthma. When a patient with severe cat allergy who doesn't live with cats enters a home with a cat acute symptoms may occur. This may include throat closure (laryngospasm). I have never heard of this resulting in death. But it's not fun.
Not likely. Severe cat allergy may cause asthma which could lead to respiratory problems. Since avoidance is a appropriate step, patients usually remove themselves from exposure as well as using controller and rescue medications. I doubt that cat exposure would ever lead to symptoms of anaphylaxis- skin, cardiac, gastrointestinal, or circulatory.