I’m actually planning on using a tweaked version of Gridder to display a directory of sites using Connections … any way to answer your question.
If you do not enter anything in a field, it will not be displayed. I would say the minimum required is a name, bio and photo.
Yes, Gridder should work just fine in a responsive theme … the theme running on this site right now is a responsive theme so you could see its compatibility by visiting the demo in different devices.
Hope that answers your questions thoroughly!