Quants, Times series : queries

I’ve got certain queries here, if any of you have understood things in a better manner, pass on the good stuff please- =================================================== 1. Unit root & Random Walk Is every AR (1) model that displays a unit root a random walk ? or is it more like all Random Walks exhibit a unit root but not vice versa ? 2. If trend models exhibit auto-correlation or serial correlation, why must one use AR models ? 3. Is the RMSE (Root of the Mean Squared Errors) for evaluating Time Series models similar to Square root of MSE (Mean Squared Errors = SSE/n-k-1) for Linear Regression models ? 4.When a Times Series variables are analyzed for Covariance stationarity and a. BOTH Variables display Unit Root AND b. BOTH are co-integrated - Why are they Covariance stationary ? Is it right to (crudely) say that co-integration “washes” out the unit root effect ? ========================================= Appreciated, thanks.