I have come across various constructs in English grammar/language like Noun,
adjective, adverb, verb, preposition, article,...How many are there in total
and do they have a special name like constructs, categories or meta-language, etc.
We generally call these "parts of speech". Or at least, that's what they were called when I was in school.
Different sources give different counts. Some include sub-types that others don't, etc. I wouldn't worry about the exact number. For example, I just did a DuckDuckGo search on "parts of speech" and the first hit it gives is titled "The 9 Parts of Speech" https://www.thoughtco.com/part-of-speech-english-grammar-1691590 while the second is "The Eight Parts of Speech" https://butte.edu/departments/cas/tipsheets/grammar/parts_of_speech.html :-D The difference is that the first includes "articles/determiners" and the second does not.
But any list should have noun, verb, adjective, adverb, conjunction, interjection, preposition, and maybe pronoun.