Hello Phew! I think that "major" in this context could come form the term "major league" which originates from "being in the major leagues" which means being in the highest-ranking league in a particular professional sport, especially baseball. This was obviously used to describe sporting achievements but if you say that "something/someone is major league" it means that it/they are very special and a shortened way of saying this is "major". So if something/someone is "major" then it means that thing/person is very special or important. I would say this is slang, though and not really proper English. If you use "major" as an adjective then it is the same as "big", "large", "huge" or "extreme". For example "major problem", "major accident", "major heart attack", "major surgery". I hope that helps!

It's a line from the movie 'Intern' right? The simple answer is that using 'major' in this way isn't common at all. We would always use it with an article preceding and a noun proceeding, exactly as you said in your examples.

Thank you all! The movie is The Intern by the way. :)

which movie?

If there’s no any noun after the adjective don’t use “a” :) but remember: major can be a noun in the meaning of military officer for example :)