Yes stationary is the assumption you have to check it first

In fact, what you need is a) stationarity for all the variables (including the "dependent" variable) or, b) if two or more of the variables are integrated (have unit roots), they have to be cointegrated. If only one variable is integrated, there is no linear relationship (in levels) between them.

The way to check stationarity is the standard unit root test (like Dickey-Fuller). There are several ways to check cointegration, but the standard Johansen test is the more common.

I would be very cautious with a working paper where they assumed stationarity (and they do not test it).

Does stationarity test should only apply on absolute numbers OR can apply on percentages, rates (Like trends of Total Fertility Rate), Ratios (trends of Maternal Mortality Ratio).

you should always test for stationarity before conducting time series analysis as non-stationary variable could cause several model mis-specifications. Usually to make sure that your results are correct, try using more than 1 test for unit root. I'd recommend ADF initially then PP or KPSS. And no it doesnt only apply to absolute numbers. it could be any macroeconomic variable for instance (they usually are non-stationary as macroeconomic variables tend to grow over time)

Srinivas,

Just like all the others have stated you need to always determine the order of integration of your variables before you run any time series (even panel data) analysis. You don't want to run into problems of estimating models with series that have no likelihood of no co-integration. Even when running models with Dynamic Ordinary Least Squares or Fully Modified OLS, you still need to determine the order of integration. You cannot measure this by mere observation of the series or merely assuming there are no unit roots.

In any case, even if you assume it, check the residuals, if you have any problem, it will be in the residuals.