i think it would be useful to have a native Greek speaker confirm the meaning of the sentence in Greek because that is what we are trying to translate from. Without knowing, i personally agree with the native speakers that there is a distinction to make if you add "a" but i don't think the Greek sentence implies either meaning specifically, so please allow answer with no 'a'
I am interested to hear from the Greek natives what about these differences. If I said "Ο στρατιώτης δεν έχει μία οικογένεια." would it be correct Greek? Would it have a different meaning than "Ο στρατιώτης δεν έχει οικογένεια."? How would a Greek express the differences we express in English by the way we use that little article "a"?
If I said "Ο στρατιώτης δεν έχει μία οικογένεια." would it be correct Greek?
This would only be correct if you followed it up with "Έχει δύο!" The only good reason why you should add μία is to use it as the numeral and make a point out of it.
The Greek phrase "Ο στρατιώτης δεν έχει οικογένεια." does not make a distinction between having "a family" (e.g. wife and children) and "family" (relatives). Further explanation or context is required.
I wouldn't have thought so - officer is αξιωματικός. Soldier implies someone of a lower rank than an officer.
As for not using an indefinite article in English, I reckon that's probably OK. It sounds a bit more American than British to me, but I have heard people use 'he doesn't have family' (especially if it's then followed by another clause).
Although I could be wrong - I'm very new to Greek.
To me (native U.S. English speaker), "does not have family" means something different than "does not have a family." With the article, the phrase suggests that the person in question does not have a spouse and/or children. Without the article, the phrase suggests that the person has no close living relatives.
"family" is a collective noun. There are not that many of them and they are easily misused by even native English speakers. The change in meaning in English (and many other languages) when an article is used or not used is subtle and difficult. If you carefully read the English grammar blogs for "a family" you will find support for "a family" = wife and kids, and "family" meaning "relatives" but even there you will not find unanimity. You can continue to use them as if they mean the same thing but you should be aware that many people will catch the implication we have described here.