Hi,
Did I put the right article for the first example and make the right choice of not put articles in the second example?
1. ... to learn to learn more about them (eg, a 'gay' community').
2. He sites examples like family and groups people (eg. 'gay' community).
You have other errors here that I have high-lighted. In addition, it would be easier to comment if you supplied a complete sentence in each case.
However, generally speaking, if community is singular as in #1, it needs an article. In #2, it seems to me that you need the plural word 'communities', in which case your choices are 'no article' or 'the', depending on context.
Best wishes, Clive