I can't do any research at the institute even though my research icon shows 0/1 and all requirements..

Sounds like it glitched. Always try force closing the app and opening it again, this clears most small glitches. You can also log out and in again as long as you have your game account bound to an external account (facebook, google play, IM30 etc.

If this still doesn't work you can contact the developers in game and hopefully they can fix the issue.