What is this seperate peace that Gene feels he has achieved? How has it affected the rest of his life?

Gene feels different emotions at different times in the novel. If you are referring to the end of the novel, I think finally Gene feels separate from Finny. The two boys had a rather unhealthy co-dependence thing going on. They lived for each other which often entailed manipulation on both sides. It isn't until Finny dies that Gene is able to be forgive himself and find a separate peace in his own skin.