Government type is displayed by the Military Advisor. In the right side window it has *So and so, Repubilc/Monarchy/etc.*. You can click on the title bar to cycle through the various civs you have contacted to see the various governments in play.
You cannot find out what they are researching directly. You can guess sometimes though. In diplomacy, ask them what they will offer for 1 of your techs. If they say *1 gold* they are likely near discovering that tech on their own. Unfortunately this will only help when you have a lead.
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