You would have to cut the floor of the cab to make room for the frame. The frame goes up around the rear axle and since the extended cab frame is longer you would have to adjust for it. Thus cutting your floor in the new cab and welding plates to cover it. Like this.
Yes and no. A body lift would give you that clearance but the body mounts are most likely not going to line up meaning you would have to use less and have the cab secured with less bolts or fab up some mounts. If you are going to do it cutting the floor will be the best way to do it.
How did the cab swap go ? I know this is a few years old thread but I'm about to swap my supercab 2wd onto my single cab 4wd frame. Hoping it comes out good, the 2wd is automatic w A/C and the 4wd is stick but no A/C so got to figure out what's gonna work with what.