word choice - Adjective or noun when referring to plural citizenship

What is the right form to use when talking about plural citizenship?
"We are Italian" or "we are Italians"? (or American, Or German or any other ending with "*an") Same issue for "Saudi" or "Saudies", "Israeli" or "Israelies", etc. I understand that one is used as a noun and one as an adjective, but which is right and why?

And on the same topic, how can for example, "Chinese", "Taiwanese" or "Japanese" be used differently for plural and singular?

And what should one do with "Korean" - is "Koreans" even valid? Somehow it sounds strange to say "Koreans".

EDIT I : as result of the comments :

I am not specifically talking about "nationality" . the same can be asked about a city:

would It be "Londonian" or "Londonese" , "New-Yorkean" or "New-Yorker" "New Yorkian" or "New-yorkese"?

..and also about non-human objects or concepts like books, food, drinks, art , company etc.

I am sorry if I combine different concepts here , But I have a difficulty in pin pointing a common logic .

Answer

To use an adjective of nationality, you can simply say

We are Italian [Japanese, American, German, Egyptian, Korean, etc.]

or

I am Italian [Japanese, American, German, Egyptian, Korean, etc.]

The fact that you are an Italian person is implied (and obvious).

If you want to stress the personhood of the individual or group, say

We are Italians [Japanese, Americans, Germans, Egyptians, Koreans, etc.]

or

I am an Italian [a Japanese, an American, a German, an Egyptian, a Korean, etc.]

Note that in cases where the the nationality adjective takes the -ese ending, as in Japanese or Portuguese, you do not add the -s to form the plural.

Finally, there is nothing wrong with saying either Korean or Koreans.

EDIT The -i ending follows the form of the -an ending: Saudi/Saudis, Israeli/Israelis, Pakistani/Pakistanis. And there are some nations for which no really satisfactory plurals or adjectives exist: What, for example, does one do when referring to people from Ivory Coast? Probably call them Cote d'Ivoirian, but that is a bastardization at best.

EDIT 2 in response to OP's EDIT 1

Since it now appears you are talking about any demonym, there is no good rule to apply except this: there is no common logic (and, indeed, perhaps no logic at all). You must learn each case individually. In America we have Chicagoans from Chicago, Angelinos from Los Angeles, New Yorkers from New York, Mainers (or Mainiacs) from Maine, and I myself am proud to be a Masshole from Massachusetts (joke!). Note that most place-names ending in a vowel can, however, take the -an ending in one form or another: Tennesseean, Georgian, Russian, Australian, etc., and in some cases you add an i before the an (Floridian, for example). Still, you still have to contend with Naples => Neapolitan, The Netherlands => Dutch, France => French, and so on.