I have now been able to take a look at your gallery and the configuration options it uses (although I do not have a Samsung S3 on which to test).
I made a test on 3G and WiFi on Android phone, I confirm that audio is playing with WiFi (but playAudioOnLoad doesn't work) I have to turn on Audio button.
Is the audio icon's status always correct, though? When you load the gallery, does the audio icon in the button bar show the 'Click to play audio' status and does a single click (rather than a double-click) play the audio? It sounds like your stock Android browser does not support playAudioOnLoad (like iOS devices) but that the Audio Button is displaying and functioning correctly.
Try a difference browser (such as Chrome) to see if this makes a difference.
Also, try setting expandInNewPage="AUTO" or expandInNewPage="TRUE" (rather than expandInNewPage="FALSE") to expand the gallery on a new page (rather than within the embedding page) to see if this makes a difference.
With 3G connection no audio at all.
Maybe this is due do with the fact that your audio tracks are approximately 7MB each and are taking longer to download over 3G. Does the gallery display OK over your 3G connection? If not, please see this FAQ for a solution.
I also notice that your gallery's Back Button icon is not visible.
The Back Button icon's color should be determined by the buttonBarIconColor but is overridden by the textColor (which in your gallery is fully transparent). Either change your gallery's textColor (so that it is not fully transparent) or remove this configuration option from your gallery's XML file and your gallery's Back Button icon should become visible.
(I have logged a bug report with the developers regarding this and it should hopefully be fixed in a future version.)