"misunderstand" is usually used in some situation that you didn't understand or a mistake in reading or listening.
If you have no idea what was said, then you would say "I didn't understand." If you believed that you had translated or heard something correctly, but it turned out that you were wrong, you would say, "I misunderstood what was said."
The noun "misunderstanding" is usually used for some situation that involves emotion or argument. "My sister and I had a misunderstanding."
For the other phrases, you usually wouldn't say "fault", as no blame has been involved.
You would say something like, "I didn't hear correctly", "I didn't say it correctly" or "I didn't say it right."