Learn Italian: Hai torto: non è vero. - You are wrong: it is not true.

In Italian, being right or wrong is treated as something you possess. You use the verb avere (to have) rather than essere (to be). So, avere torto literally means "to have wrong," just like avere ragione means "to have right" (to be right).

Could I say non hai vero to mean "you are not right"?

No, because vero means "true" and is an adjective used to describe facts or statements, usually with the verb essere (like è vero - "it is true"). When talking about a person being correct, you must use the noun ragione with the verb avere (hai ragione - "you are right").

Where is the word for "it" in non è vero?

Italian routinely drops subject pronouns. While English requires "it" as a placeholder subject ("it is not true"), Italian simply uses the conjugated verb. È alone already implies "it is" in this context.

How would I apply this lesson's indirect speech rules to report that someone was wrong?

If the original direct statement was in the passato prossimo (e.g., "Hai avuto torto" - "You were wrong"), you must backshift it to the trapassato prossimo when reporting it in the past. So, "He said that I had been wrong" becomes Ha detto che avevo avuto torto.