You seem to be finding some things puzzling that are actually made explicit in the book.
By Gurgeh's request? No, not at all. It's quite clear that Gurgeh had no idea of the drone's real identity.
Yes of course Flere-Imsaho's personality was faked. He was an expert SC agent: the bird-watching was just a cover, as we learn in the sequence when he takes Gurgeh for a tour of the seedy side of Azad civilization. Similarly, yes of course the blackmail was made up: Mawhrin-Skel was never a failed SC agent, he was working for them the whole time - in fact that whole bitter personality was just as much an act as FI's fussiness.
As to the reason for the whole game plot, that's just the way SC works: they never do things by violence if there's any other way. The game was the way they'd agreed - it wasn't that they'd invade if they won, but that they'd simply take over, having - in the Emperor's eyes - shown that their way of life was better, by having won the game.