No he didn't. Coen did, and he died there. Geralt was in Nilfgaard at the time rescuing Ciri.
What support do you have for him hating them? He may not like Nilfgaard, but then again Geralt looks down on everything political.
Then there is a continuity issues because Shani in W1 tells Geralt that she was there with him at Brenna. And the dwarves on Iorveth's path before going to the mines talk about Geralt being with them at Brenna. So the games say Geralt was at Brenna.
I gave you numerous reasons why Geralt would hate Nilfgaard yet your response is he hates politics? You did not provide any proof or facts that say Geralt didn't hate Nilfgaard nor did you counter my facts.
Because the confession was just another part of the Nilfgaardian plot. They'd got rid of some kings, the final step was to make sure the Council of Mages wasn't formed. So the Nilfgaardians presented him at the Conference, claiming that he'd been "captured trying to assassinate Shilard" (pure BS), and he gives a confession that's only partially true - he killed the kings, he was employed by the Lodge, but he missed out the bit that his true employers were the Nilfgaardians.
Once the conference was over and he'd given his speech, he wouldn't have been a prisoner any more, so he's free to turn on the Nilfgaardians and rescue Triss, maybe because he has a thing about Sorceresses, or because he feels guilty about bringing her into it (he knows she wasn't part of the conspiracy), or as an attempt to appease Geralt, whichever explanation you think fits.
Huh? So they free a kingslayer? Yet they actually try to arrest Sile? This makes zero sense. He's under arrest, he confesses and they let him go free? Please help me here. Explain this.