My friend has been in the hospital for 12 days. She can't breathe, she hurts all over, and her oxygen keeps dropping. What could this be?

Possible lung clot. She needs a very urgent evaluation for clot in the lung. Even if this is not the case, any reason for difficulty with breathing like pneumonia, need to be evaluated as soon as possible.
Many possibilities. There are a number of possibilities including flu, pneumonia and severe infection. The symptoms you describe are not specific for any one possibility.
Severe illness. This is obviously a severe condition that can be caused by a great many illnesses. Your best source of information is from your friend's health care givers.