I think the word you are looking for is "colloquial". When two people are communicating they are expressing a feeling or an idea. The mathematical correctness of the expression isn't important.
I don't think either of these are grammatically incorrect.
In the first example "how are things going" is an idiomatic expression that is used as part of a social ritual. The response is another idiomatic expression. This is a typical greeting ritual.
The phrase "A big nerd is just who I am" is perfectly correct in English. When Darth Vader says "Luke, I am your father", it is the same sort of thing.