Corner Rounder gives you the ability to set different radius values for each corner individually, while the basic Rounded Corners tool applies the same radius to all corners.
For iOS-style app icons, use a square image and set the radius to about 22% of the image width. For Android, use a slightly smaller radius around 15%.
Yes! Switch to "Individual" mode to set different radii for each corner. You can even set some corners to 0 while rounding others.