Yes, to all your questions. And the Zip manual thread/manual link, for your questions concerning the device: http://forums.sandisk.com/t5/Sansa-Clip-Zip/Clip-Zip-User-Manual/td-p/242618.
Also, I don’t know that I really would consider the battery in the Zip ‘weak": 12-15 hours of play, when new. (But, yes, the Sport’s battery lasts longer.)
