Learn Farsi: پیک همیشه صبر می‌کرد تا نامه نوشته می‌شد. - The messenger always used to wait until the letter was written.

This sentence uses the past continuous passive to show a repeated, habitual action. It combines the past participle نوشته (written) with the past continuous of شدن (to become), which is می‌شد. Because the messenger always waited, the writing of the letter was also a repeated past event, so we use می‌شد instead of the simple past شد.

Usually تا (until) is followed by a verb in the subjunctive mood. Why doesn't that happen here?

You use the subjunctive after تا when you are talking about an action that hasn't happened yet (like "wait until the letter is written"). But because this sentence is reporting a habitual fact that already took place in the past, we use a past tense that matches the main clause. Since he "used to wait" (صبر می‌کرد), the letter "used to be written" (نوشته می‌شد).

Does صبر می‌کرد mean "was waiting" or "used to wait"?

It translates best to "used to wait" in this context. The Farsi past continuous tense (a verb with a می- prefix in the past) covers both ongoing background actions ("was waiting") and habitual past actions ("used to wait"). The word همیشه (always) is a big clue that this describes a repeated habit.

How is the word نوشته formed?

It is the past participle of نوشتن (to write). You make a past participle by taking the simple past stem (نوشت) and adding an to the end. Every passive verb in Farsi requires this past participle combined with a form of the auxiliary verb .