@ daniel, Gina
The user search category drop down is currently a feature reserved for the premium sold here. Presently, the free templates only show the photo, not the logo.
That said… this Friday, if I get it done, there is another update for Connections planned. It is a rather significant update too. The big new feature is integration with the WordPress Customizer to configure the templates (point and click with real time preview of the changes). Most of the free templates will be retired and removed since they will no longer be relevant due to the template customizer. The important bit and why I bring this up is one of the many options you’ll be able to configure in the free default template is whether the photo is shown or the logo is shown.
I hope that clearly answers both your questions.