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To answer just the first question, yes there is a different set of critical values. The built-in Engle-Granger test from a group object performs the relevant regression and test computation. I believe this set of critical values is the one tabulated by MacKinnon: Critical Values for Cointegration T...

I am examing if there is a cointegrating relationhip based on the Engle-Granger approach between EUR/USD and GBP/USD currency series. Applying the ADF test in the log-price and log-return series I found out that the level series are both I(1). Then I regressed the logeuro levels on the loggbp levels...