Article with adjective + unique noun

Dear English Speakers,

I asked earlier about the use of articles before adjectives that precede unique nouns (the sun, the sky etc.). It was confirmed that a/an/the can all be used depending on the context.

Does the same apply to unique nouns when they apply to people? 

1. John, who's been in a relationship with one woman, suddenly shows up with another girl. I ask my friend:
"Is she a new girlfriend?"
"Yes, I think she is a new girlfriend."
(There is no information that he changed girlfriends and there're many girlfriends in the world in general, so I think "a" is better.)

2. I enter my office and see there is a new man sitting in the CEO's office. I am surprised.
"Who is he? A new CEO?"
"Yes, he is a new CEO".
(Still the indefinite article. Many CEOs in the world. I did not name the company).

3. A former US President writing an autobiography is ruminating about the period after he got elected:
At the time, I was a new president. I knew nothing about running a country.
(I use the indefinite article because there are many presidents in the world and were so at the time of his election).

4. Same thing as #3, but now he writes:
At the time I was the new US president. I knew nothing about running a country.

(I think the definite article is better because there was only one new US president at the time. But I am not sure)

The info I found online is very conflicting. My own understanding is that girlfriends, CEOs, there are many of them in world, so "a" in my examples is more correct. But if I were to "Microsoft CEO" or "US President", the definite article should be used. There's only one.

Can someone please help and explain?? I would be so grateful.

Gudrun