The girl has long hair and it is quite a difficult problem are the correct sentences.

Grammar is spelled with an "a" near the end (-ar). "The girl has long hair" is the correct version. This is because you're referring to the entirety of her hair (all her hairs on her head), and in this meaning "hair" is an uncountable noun or 不可數名詞. Uncountable nouns do not usually take an indefinite article, especially when they're the object of a verb or a preposition. Some examples: "I have short hair" (not "a short hair"). "I see dry grass on the other side" (not "a dry grass"). "It is quite a difficult problem" is better. "It is a quite difficult problem" is also correct in some way, but it's very uncommon, and sounds rather strange. This is just how the word "quite" happens to be used in noun phrases, appearing before an article (either "a" or "the"). More examples: "It was quite an exciting book." "It was quite a turn" (that is, the turn was very quick and sudden). "He was quite a student" (maybe a very good student, maybe a very bad one). "It was quite the predicament." "They are not the same."

差别在于 - 那位女孩有一根长发 vs 那位女孩有长发。

thank u!

Grammer => grammar The hair on a person's head is uncountable, so cannot say "a long hair", just long hair.