How can I use quizzes from one course in another course?

There are two options:

1) You can publish the category which the quiz questions are currently in. However, this will make your category questions visible, usable and editable by any teacher in Moodle. This is not recommended, and will not work if you are using images in your questions.

or

2) You can create a backup of the first course, selecting just quizzes (and course files, if there are any images in the quiz). You can then upload this file into your second Moodle course and restore it, “adding to the existing course”. (See the Guide on Backing up and restoring Moodle courses for further details on this.

How can I backup forum posts?

Unfortunately there is no easy and efficient way. The only options currently available are:

1. Display discussions in nested form and copy and paste them into Word (would need to be done on a per-discussion basis)
2. Backup all the forums in a course (using the backup utility in the admin block). This produces an XML file from which message data could be extracted but not easily.

1. is easier, though could be time-consuming if there are a lot of discussions in a forum.