I think Diplo screen need complete redesigning to be the honest. And I like your suggestion.
1. Should not see civs of each player until they have been scouted.
2. Maybe see info about your allies after you have research Cartography (expanding on jonbaier's idea).
3. Tribute needs complete overhaul, the way the buttons work, everything, (and would be nice to have tribute penalty at first that can be remove with tech, like in AOE franchise).
4. Overall the window is too small for new stuff/updated overhaul.