I don't know anything about protection from freezing in colder areas with frost lines, so I can't comment on that.
As far as the copper, that should work well for what you wish to do. Unless the soil is really corrosive, you shouldn't need to run the copper inside of a sleeve.
If you use 4" pipe, the T fitting that you have circled in your last picture will have to be changed out to a 4" T. And if you use white (PVC) pipe, you will not be able to glue the black ABS and the white PVC pipe together, so you will need to plan for a mechanical joint there, perhaps a rubber coupling.
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