Yellow or greenish chest mucus is generally a symptom of infection and is often a sign that you should go to your doctor. Chest mucus that contains blood is often a symptom of a more serious infection such as pneumonia or TB, and large amounts of blood in the chest mucus should be seen as a medical emergency.
In California, your residency depends on how long you live in California, what ties you have to the state and local government and whether you are financially self-sufficient. You must be physically present in California for 366 days to become a state resident, except for brief absences such as vacations.
There is a difference between being resident, ordinary resident and permanent resident. From these the most strict one is permanent resident. As an EU/EEA citizien you get permanent resident (and can apply for proof) after 5 years of continuous living (meaning you can be absent from the UK for at most 540 days total, 180 days at a time) in the UK. As an EU/EEA citizen however you might not need to obtain permanent residency, as it doesn't really add anything to your general rights.