Live conversation (also called synchronous communication) is possible with the Moodle Chat Activity
Generally, no. However, some areas are more private than others and certain information will be kept from other Moodle users (for example, fellow students). An exception to this is the Feedback activity which can be set to be anonymous.
Yes, you can upload video files like any other file resource up to the maximum size allowed by your Moodle site. As video files can be large this probably means that they will need to be small, short and of low resolution. You are strongly recommended to encode video files in Flash Video format (see http://en.wikipedia.org/wiki/Flash_Video). For larger video files you may wish to consider using the University's streaming media services. You are strongly advised to seek advice from the LTU (email@example.com) if considering using video in your course.
Yes. Quizzes in Moodle are made from banks of questions that you create. You can then sort them into categories which can be 'published'.
By default all questions that you create will go into the "Default" category, but you can (and probably should) create new categories to organise your questions. A questionbank can be shared with other courses - this must be done by your Moodle administrator. If you wish to share questions with another moodle site, a category can be exported. There are a number of formats but the Moodle XML format is the most comprehensive. These can then be imported at the other site.
Uploading files in Moodle is, unfortunately, not as easy as weí would like (However, feature requests for drag and drop in future have been made). You can upload several files to Moodle at once if you use zip. Zip the files on your PC and upload the zip file to your Moodle course. In your course sites files in Moodle, you will see an "unzip" option next to the file. This can be used to transfer (for example) whole websites into Moodle.