I have the Chevy Duramax, but the dodge should be close to the same:
Engine oil is what it is, but mine holds 10 quarts with filter change. The filter is a sunk cost, so you are really only paying for the additional amount of oil over a gas engine. My 6.2 gas engine in my other truck holds 8.5 quarts, so for me the cost is only about six more dollars, and the Mobil filter costs the same for the gas or diesel engine. Depending on driving style and if you are pulling anything, you should get around 6000 miles before a change is necessary.
DEF is about 8 bucks for a 2 1/2 gallon jug, and my truck goes through about seven gallons every 6-7 thousand miles. I would assume the dodge is pretty close to this amount also, but not sure. So, a penny or two per mile.
Fuel costs are more, but to me the difference is not too bad, and at times up here in Chicago I pay less for diesel than gas. There is no substitute for the torque you get out of a diesel. Drive your new addition for a couple of months and see how you like it. If you do your maintenance yourself, oil changes are not that much more than a gasser, and the DEF is a once in a blue moon type of thing to deal with.
As for fuel additives, I too add DieselKleen to my tank about once a month or so, and I use biodiesel (sold at BP stations). The truck always runs really smooth.
Sorry for the loss of your dad.