Scarf joints _can_ be used to make longer horizontal beams and rafters out of shorter pieces of wood. Unless the challenge of the task is really, really, attractive, and you are very confident of doing ti well then I agree that you should just use whole stock
You can make longer studs from the shorter pieces using mortise and tenon joints. Cut the tennon on the lower piece and the mortice in the bottom butt of the upper piece. However half-lapping or just butting them with additonal pieces nailed to either side will do just fine.
Again, it is a question of how fancy you want to get in addition to being frugal.
Well, why didn't you say so before? You can saw the slats off in between the stringers and use those to overlap the splices on the studs. If you can seperate the slats from the stringers without breaking them (often it is easier to pund the nails through the slat rather than pulling them out) then you can use those for the rafters too.
You will need to plane them to uniform thickness and then laminate them face-to-face, staggering them so that no two places where they are butted end-to-end are accross the same section of the rafter. You will need to use at least three 'layers' of slats per rafter, and maybe four to assure that the minimum thickeness accross any section is 1 1/2". THis will also take a lot of glue.
Do you have a source of cheap glue?
But you get to select it.