I'm living in a non-English-speaking country, so I usually contact English only through mass media (drama, for example). I've seen some use cases where no is used as if it's interchangeable to not a, like in the example "I'm no Superman" from the drama Scrubs, but I'm not sure if it's a standard (or formal) usage or not. Is there an underlying grammar behind this, or is it just a slang?
The underlying grammar is that "no" can be used a determiner. As a determiner it means "not any" or sometimes "not allowed" or "not at all a". So we can say, with "no" as a determiner:
There is no water here (not any)
There is no smoking in the building (not allowed)
He is no fool. (Not at all a)
It is not slang, and can also be used in formal situations.