1. There are a few differences between Cointegrated ADF test and Johansen test.
First of all, the former is only suitable for a pair of two time series, while the latter is also applicable for cointegration test of any number of series.
Secondly, ADF test will suggest different test results when we switch the sequence of the inputs, while Johansen test is order independent as the latter is based on the eigenvector decomposition. Specifically, When performing Cointegrated ADF test, it first determines the optimal hedge ratio by running a linear regression between the two price series, use
this hedge ratio to form a portfolio, and then finally run a stationarity test on
this portfolio of price series. Therefore, using asset A as independent variable and asset B as dependent variable will likely to yield different results as the opposite case. Usually, only one hedge ratio among the two test cases can lead to a stationary portfolio, and one may need to run ADF test for both cases in order to find all possible hedge ratios. For the case of Johansen test, all the hedge ratios that can potentially lead to stationary portfolio for the $n$ assets are found all at once, which are the eigenvectors of the coefficient matrix.
2. It's normal to find conintegration pairs that are demonstrating false statistical significance.
Especially, if you pull out a big universe of assets, and then performing pair-wise conintegration tests. By testing too many hypothesis, we also increase the likelihood of witnessing a rare event, and therefore, the chance to reject the null hypotheses when it's actually true (type I error). Bonferroni correction is an effective way to address this issue.
