Yes, the Color Contrast slider is similar to a certain range of the Convert > Hue slider, but not identical. It allows stronger effects and simulates a Polarizer filter, which is less convenient to do with the Convert > Hue slider.
The Paper Density slider works in connection with the Multigrade slider. They both influence the look of the Multigrade effect. Needless to say that the Multigrade effect of B/W Styler is only a approximation of the effect that you can get with different photo papers. It also lets you achieve effects that are not possible by selecting a certain photo paper.