Your English is great. If you don't mind could you talk about the use of the article "the" in your native languages? (Standard Arabic, a dialect and perhaps others?)
I personally feel strongly (although I am maybe the only one) that people should refrain from talking about "the singularity" since the word "singularity" covers several very different and incompatible ideas. I think it often causes confusion the way people sometimes talk about "evidence for the singularity" or "the likelihood of the singularity". To talk about the idea of "a singularity" is better, much as you said, or sometimes "a technological singularity".
My native language is Persian (Farsi). There is no definite article in Persian and the specific object/ person/ idea which a noun refers to is determined from the context.
I agree with you about the ambiguity of the word "singularity". Not only there are different definitions for "singularity" in AI, the term is also applied in other contexts (e.g. economic singularity, gravitational singularity). I think, as you said, talking about "a singularity" is more appropriate.