I've never towed with a super duty, but I have towed with other lifted trucks. 4" isn't bad, but obviously will require a drop shank. One thing you would want to consider is your tire load rating. A 35" flotation tire will have a pretty tall sidewall, they are available in E load rating, but I'd be concerned about sidewall flex.
I don't think you'd see much difference on fuel mileage with the diesel, but you will need to get the computer flashed for the new size or you'll have problems with the shift points, speedo, and ABS.
2013 Alpine 3500RE
2019 Silverado 2500HD Duramax
U.S. Air Force Retired (25 yrs)