turning garage into room and two story
Your post is pretty confusing to me, let me see if I get it. The interior wall you want to move five feet - is this inside the house, or inside the garage? Is it a load bearing wall? Does moving the wall have anything to do with your garage project?
You want to add a "two story" above the garage. I don't quite follow, you want to add two stories of living space above the garage (making it a three story structure)? Or you want to convert the garage two stories of living space? Then you add after you close it in. After you close what in? Do you have an open garage at the moment?
As to converting the exterior wall to 2x6 rather than 2x4, that is usually done for insulation reasons. Are you thinking this is needed for structural reasons?
Any conversion of garage space into living space will require a permit from the local building inspector, and usually triggers a whole series of changes best discussed in advance with the building inspector, typically including egress issues, lighting, plumbing, heating requirements, possibly structural issues. Usually a good idea to bring a box of donuts over to the building department to discuss the project, my guess is there will be a number of significant issues worth settling.