So, you are saying we CAN host it ourselves and student's won't have to start from the beginning if they stop in the middle of a test?
Yes- but that *could* depend on quiz settings - e.g. set the quiz so that "Each attempt builds on the last", for example and students will always see their previous questions and answers. If your quiz has a time limit - when the time is up the student is finished and then would have to start again, etc. There is more information here:
Is there a Moodle for Dummies or what would be the best resource for someone who is brand new with Moodle?
The Using Moodle book is a quite good place to start. Many Moodle Partners also offer excellent online and face-to-face training. For example, we have a series of courses on Moodle: http://remote-learner.net/training