Yes. Set showSmallThumbs="FALSE" and showThumbsButton="FALSE" in your gallery's XML file to disable the thumbnail page and button in Small Screen Mode (which is used by default on mobile devices).
In order to use AutoPlay, set enableAutoPlay="TRUE" and autoPlayOnLoad="TRUE" to start AutoPlay automatically when the gallery loads. You may also wish to set showAutoPlayButton="TRUE" to display the AutoPlay button and allow users to switch the AutoPlay functionality on and off.
You can choose the first image to be displayed in the gallery by setting the firstImageIndex configuration option.
The full list of 'Juicebox Configuration Options' can be found here.
Certain options are available in Large Screen Mode only (and are marked as such).
For more information on Screen Modes, please see here.
If you like, you can force the gallery to be displayed in Large Screen Mode on all devices and in all browsers by setting screenMode="LARGE".