I am a U.S citizen and I would like to know the procedure to go about applying for an E.U passport.
And is it a different procedure if you are visiting, medical treatment, playing a professional sport?
Finally, Is china a member?

If you are a US citizen, you will need a US passport. Do you have a dual citizenship in a nation who is a member ?

I have a U.S passport, but I do not have dual citizenship with a country that is a member

I have a portuguese passport that has expired just recently and I am based in the UK.How do I apply for a renewal?