By definition, cash on cash is the before tax cash flow divided by the equity investment, however I have also been told to model CoC returns inclusive of property taxes since I like the metric to represent cash as truly possible.
Since NPV and IRR analysis are both found using free cash flows, you should model them in the same way as you measure CoC. I recommend looking at it both ways to see how much of a difference the tax makes.
Inflation won't matter in a Cash on Cash analysis, since its purpose is to give you a picture of how much actual cash you are receiving compared to your equity. However, you can note it when you find the IRR and simply subtract your predicted inflation rate from the IRR as the cash you receive further in the future will inflate away more. Although I see why you are curious about its effects, inflation adjusted IRRs are not generally used in a commercial real estate analysis (especially given the current low-inflation environment). The most important thing is to make sure you do it the same way between each pro forma so that you can make an accurate comparison. Different firms do cash flow analysis different ways, but each one makes sure to compare apples to apples.