Yes. It's correct. When relating the plot of a book, film, TV show, etc. present simple is generally used.

Yes. Stripped of all its adjectives and subordinate clauses the sentence is "The story follows a girl who eventually experiences a mental breakdown." and that sounds perfect. Present tense can be used for present, future, and timeless events: "I see a dog" (present) "Tomorrow I see a dog" (future, because of "tomorrow") "Sometimes I see a dog" (timeless) For your sentence, you have many other choices: "The story follows a girl who eventually will experience a mental breakdown." "The story follows a girl who eventually experienced a mental breakdown." "The story follows a girl who could eventually experience a mental breakdown." All are correct, but Simple Present would be the default unless you had some reason for saying it a different way.