One option is to look at the set membership information associated with "BAD" target value.
Which quality numbers are only associated with that label? Which quality numbers are never associated with that label? Which quality numbers are associated with that label and other labels?
I'm not very knowledgeable about this but here a some ideas:
Statistical testing: in order to know whether there is any statistical difference between the values in two categories, one can use the Student t-test (for normal distributions) or the Wilcoxon test (for any distribution).
In the case where there is a significant difference there are methods to ...
Yes you have to remove one of them. For example when you plot a heatmap and notice that 2 features A and B have a correlation value of 0.91, remove one of them as removing both of them will lead to information loss.
After removing one of them, again plot a heatmap of the remaining features and you'll notice the correlation values of other features have ...