No that is quite literally exactly what happens in the book. He reaches in and gouges out his eyes. If anything the fight on TV is less gruesome. In the books Gregor cuts a bystander's head in half because he got in the way.
I fell in love with Oberyn in the books, but I have to say Pedro did an amazing job. I couldn't have asked for a better actor. He is easily in my top favorite characters now where he was on the bottom of that list before Pedro.
Not really. If anything Oberyn's death fucks with Doran's plans. It spurs Arrianne and the sand snakes into action, sure. But they all get imprisoned and Arrianne nearly kills Mycella. If anything Oberyn's death nearly gets Dorne fucked hard.