(Meliora experience?) - meaning of Prompts

I know that it might sound crazy but I am not just getting the thing what they want out of it. Couldn't make out some of the meaning at all.

The University of Rochester is one of two universities listed by The Carnegie Foundation for the Advancement of Teaching as arts-and-science focused, medium-sized, and highly residential, with comprehensive PhD programs, medical schools, and very high research activity. Both offer undergraduates an unusual degree of freedom in their curriculum. Which of these characteristics (or others) are leading you to apply to Rochester? In this Prompt, it's stating that both offers undergraduates facilities. But I can't make out which are the two!

Meliora: ''Ever better'' - The University's motto directs our focus toward continual improvement through learning, discovery, creativity, and enterprising collaborations among people with different points of view. Describe a ''Meliora'' experience from your life. Didn't get the meaning at all!

Make a rational argument for a position you do not personally support. For clarity, please state your true opinion first and then argue the opposite position. Consider an issue that has affected you personally. Should I just state something and begin arguing as another person? How should be the pattern of writing? Should it write it as dialogue between me and someone else?