General question on EDA, correlations, classification, ML
If the relation between predictors is nearly 0, it's always better to drop that feature, the caveat here depends on the domain knowledge you have. 

Did you check the correlation between B and the target variable and also A and target variable? if it's negative drop it, If it's significantly high .i.e greater 0.7, use that as your feature.

Yes, pair plots and scatter plots are really important, but it would be tedious to plot features with 150 variables.