you are going to have to do the witerun quest before you do the peace treaty. its a glitch it happened in my game too only with the jagged crown quest. as soon as you complete the current objective you should be able to talk to ulfric and then put the rest of the civil war quests on hold.
(btw, the peace treaty is impossible once you choose sides in the war, from posts I've read. I mean, how can you negociate a fair peace deal when you have sworn loyalty to one side.)
not necessarily. when i did it after joining the stormcloaks tullius just mentioned how he was disappointed at the fact that I was biased and was upset that he agreed to come here knowing my stromcloak ties. he accepted the treaty anyway though.