Lernt man in einem Kurs zum Farsi lernen auch die persische Schrift?

Do you also learn the Persian script in a course to learn Farsi?

Yes, usually yes.

In introductory Persian courses, our Latin alphabet is often used at the beginning to reproduce Persian/Farsi, but this is usually only until the whole Persian/Arabic alphabet has been taught and practiced in the course. Then you continue with the new alphabet and read and write from right to left.