What version of Premiere Elements do you have and on what computer operating system is it running?
In Premiere Elements 12 Editor and earlier version Editor there is no choice for "random transitions" under the Transitions category.
If you have working in the Elements Organizer that comes with these versions, you will find the Random Transition
choice in the Elements Organizer Slideshow Editor.
In Premiere Elements 13 the same holds for "random transitions" choice in the Premiere Elements 13 Editor.
And in the new Elements Organizer for 13, the user has no control over what transitions are used and how they
are placed - the user is at the will of the theme selected.
Please supply more details so that you can fine tune the reply.
Add On...there is the manual way, different transition of your choice applied by you one by one by one....
As for the music part of your question, that will also require details on what program and version that you are working in...
classical Elements Organizer Slideshow Editor Fit Slides to Audio (versions before 13) or use of Smartsound (as heard in version 11) or Music Score (as heard in versions 12 and 13) which are based on special soundtracks created be used so that you can vary the soundtrack's duration without affecting the music arrangement.
I just upgraded to Photoshop and Premiere Elements 13 and running 64 bit on Windows 7 OS.
Thanks for the reply with your program and computer additional details.
What I wrote previously would seem apply.
If you have any questions on what I wrote or need clarification, please do not hesitate to let me know.