There are functions in R (e.g.,
adf.test) which have null hypothesis of unit-root in the process ($H_0$: there is a unit root). Does this null hypothesis mean "the process is difference stationary"? If yes, what is the order of difference required to make it stationary?
Well, for an $AR(1)$ process, yes, a unit root means the process is first order difference stationary. How about for a $AR(p)$ process?