First some quick preliminary remarks....
Premiere Elements 12 on what computer operating system? And, have you updated 12 to 12.1 using an opened project's Help Menu/Updates. Among other things, it will get rid of the Text/Style issue that exists only in the 12 Expert workspace.
Then your immediate question... You cannot do what you want to do in the Premiere Elements Editor...all transitions will be the same when you apply them more than one at a time. But...
Details for "But"....
As for the question that brought you here, in Premiere Elements 12/12.1 Editor, you can apply the same default transition to more than one at a time by selecting the photos and using Timeline Menu/Apply Default Transition. There is a large assortment of video transition, but none is a random transition. To create you randomization of video transitions, I guess you could do the Timeline Menu/Apply Default Transition in scattered batches. Still a lot of clicking.
There is a possibility whose pros and cons you might want to explore...get your photos into the Elements Organizer 12/12.1 Slideshow Editor, set the transition for Random in preferences there, open your selected photos to the Elements Organizer Slideshow Editor, output the slideshow with it random transitions to the Premiere Elements Editor with the Elements Organizer Slideshow Editor Output = Edit with Premiere Elements Editor. When the slideshow arrives in the Premiere Elements Editor, it will be in a non wmv video format. But, if you right click the video formatted slideshow and select Break Apart Elements Organizer Slideshow, the slideshow is broken down with its random transitions intact.
Please review and consider, and then let us know if any of that worked for you.