How can I find out which research agreements I, or anybody else, has active? I can't seem to find a screen that has a list.
Click on the Diplomacy icon (top right) then on the Diplomacy Overview button - it should show on here (on left hand side) if you have any Research Agreements in place. I dont think there is any way to see other civs Research Agreements, only your own.
The diplomacy overview should have it. Unfortunately, it lists things in a non-intuitive manner (it lists the turn the agreement started on, I believe?) so once you know the start date, you have to calculate the intervening years (and thus the end date) on your own.