1) Test whether MU(residuals) is I(0). If not, take the first difference of all variables first, they regress the first differences

2) an AR(4) process, yes it confirms the AR(4)

For the first question,You should use the ols to obtain the residuals,then to test whether the residuals series is stationary or not.If it is stationary,the dependent and independent variables are icointergrated.If not,you shoud use the first difference of these variables to regress.
For the second question.The ACF series suggest that this series is stationary,probably with seasonly mode and the PACF series manifest  an ar(4) or sar(4) model is suitable for this series .

第二题，为什么不是 ma(4) 呢？

有文章解释第一题 可以这样子做：Tests by Engle-Granger involve 1) unit root tests, 2) estimating an OLS model on the I(1) variables, 3) saving residuals, and 4) testing whether the first order autocorrelation coefficient has a unit root (they are not cointegrated) or not (they are cointegrated), Δet = a1et-1 + εt.

但是我没有很明白，不知道您可以解释下吗？

有文章解释第一题 可以这样子做：Tests by Engle-Granger involve 1) unit root tests, 2) estimating an OLS model on the I(1) variables, 3) saving residuals, and 4) testing whether the first order autocorrelation coefficient has a unit root (they are not cointegrated) or not (they are cointegrated), Δet = a1et-1 + εt.

但是我没有很明白，不知道您可以解释下吗