Learn Portuguese (Portugal): Adeus, senhor médico!

In Portuguese, it sounds too direct or even rude to address someone using just their profession. Adding senhor (sir) or senhora (madam) before the job title makes it polite. While in English we just say "doctor", in Portugal it is normal to say the equivalent of "sir doctor".

Could I use doutor instead of médico here?

Yes, and it is actually much more common to hear senhor doutor when speaking directly to a doctor. The word médico specifically means "medical doctor" or "physician", while doutor is a broader title of respect used for doctors, lawyers, and people with university degrees.

Is adeus the usual way to say goodbye?

adeus is a slightly more formal way to say goodbye, and it is often used when you are not going to see the person again for a while (it translates literally to "to God"). For everyday or casual goodbyes, people usually say tchau or até logo (see you later).

Why isn't médico capitalized?

In Portuguese, words for professions, titles, and nationalities are written in lowercase. You only capitalize them if they are the very first word in a sentence.