Which one of the given sentences is not grammatically correct?

The correct answer is Option (2) → She came while the meeting was over.

While means during the time that something is going on, so it needs an action in progress: "She came while the meeting was going on." "The meeting was over" describes a finished state, so it needs when or after.
Corrected: She came when the meeting was over.
Example: The phone rang while I was having dinner.

Why the Other Options are Incorrect?

Option 1: Copper is a useful metal. — Incorrect. Correct use: the sentence is grammatically correct: a singular subject, the verb "is", and "a" before the consonant sound of "useful".

Option 3: This is the house where I lived for ten years. — Incorrect. Correct use: the sentence is grammatically correct: where rightly introduces a clause about a place, and the simple past fits a finished period of living there.

Option 4: The doctor discharged the patient from the hospital. — Incorrect. Correct use: the sentence is grammatically correct: one is discharged from a hospital.