The dot plots should show some separation of the two groups. Second, try a simple univariate logistic-regression using the binary variable as the Y...

The dot plots should show some separation of the two groups. Second, try a simple univariate logistic-regression using the binary variable as the Y variable with each individual predictor. Third, although it seems odd to do so, convert the binary response variable to a 0/1 continuous response and try some of the standard smoothing methods, such a spline fit to investigate the general form of the response. Does it look logistic? Are quadratic terms needed?