Hi Pres, welcome. A kitchen backsplash is considered a dry area and really doesn't call for any waterproofing but you can add a waterproofing if you want to.
I try to avoid cutting the sheetrock horizontally along the countertop, it makes the backsplash real weak. Blocking helps of course in case the sheetrock has to be replaced. Usually I would apply a thin coat of thinset to the back splash to fill in any holes and divots. A small amount of floating can be done with thinset if there is a crooked stud. You can tile right to the sheetrock if you can get it smoothed out.
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