Is every non stationary series convertible to a stationary series through differencing Can every non stationary time series be converted to a stationary time series by applying differencing? Also, how do you decide the order of the differencing to be applied? 
Do you just difference with intervals 1,2...n, and perform unit root test of stationary each time to see if the resulting series is stationary?
 A: The answer by whuber is correct; there are lots of time-series that cannot be made stationary by differencing.  Notwithstanding that this answers your question in a strict sense, it might also be worth noting that within the broad class of ARIMA models with white noise, differencing can turn them into ARMA models, and the latter are (asymptotically) stationary when the remaining roots of the auto-regressive characteristic polynomial are inside the unit circle.  If you specify an appropriate starting distribution for the observable series that is equal to the stationary distribution, you get a strictly stationary time-series process.
So as a general rule, no, not every time-series is convertible to a stationary series by differencing.  However, if you restrict your scope to the broad class of time-series models in the ARIMA class with white noise and appropriately specified starting distribution (and other AR roots inside the unit circle) then yes, differencing can be used to get stationarity.
A: No.  As a counterexample, let $X$ be any random variable and let the time series have the value $\exp(t X)$ at time $t$.  The $k^\text{th}$ difference at time $i=0, 1, 2, \ldots$ is a linear combination
$$\Delta^k(i) = \sum_{j=0}^k w_j \exp((i+j)X) = \exp(iX) \sum_{j=0}^k w_j \exp(jX) = \exp(iX) \Delta^k(0).$$
for coefficients $w_j$ (which can be computed but whose values are irrelevant for this discussion).  Unless $X$ is constant, the left and right sides have different distributions, proving the $k^\text{th}$ difference is not stationary.  Therefore no amount of differencing will make this time series stationary.
