How should I relocate my shed?
I think:


No, it is not a good idea. You can expect all the difficulties of renovation, new construction, and building relocation, combined. Perhaps also conflicts with land use regulations as well. Without tying the roof to the adjacent structure, expect water damage to both the shed and the home.
Support for the shed should be suitable for the soil and drainage conditions local to the site. A proper foundation would be the preferred solution. Whatever is constructed should be in accord with current building codes and meet the requirements for wind and seismic forces.
A concrete slab might provide better long term performance.
See answer 3.