
I've heard (and read) very often "We are family." Has this expression the same or a different meaning? Are both fully correct?

An interesting question. Esperanto doesn't feel the need for indefinite articles, but English may possibly communicate some subtle change of meaning between the two sentences. I think the person who says "We're a family" is thinking of one specific family — usually the nuclear family of the person himself, his/her siblings and one or both parents, or of the person and her/his spouse, along with their children.
The non-article sentence "We are family" reminds me of a popular song: <https://en.wikipedia.org/wiki/W...amily_(song)>. The song can be heard to refer to the entire extended family of humanity in general — at least that's the impression it makes on me.
Also, sometimes the sentence "We're family" (without the article "a") can be given, I think, as a justification for why one should tolerate or excuse a relative's occasionally boorish behaviour — behaviour we might not so readily tolerate in a person to whom we were not related.

A well chosen list. I'm not opposed to the way the word "family" is used in most of them, particularly where it's preceded by "like" or "practically"; all those sentences sound perfectly natural to my ears. Your mileage may differ.
In the three following examples, however, I believe the word would indeed more likely be "relatives".
[#2361856] I'll go to Boston to be with family. (CK) *audio*
[#2359502] I have family in Boston. (CK) *audio*
[#2958133] Tom should be with family. (CK)
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