Yes, Boolean operations on shapes are supported. Select the shapes/paths, and use the "Merge selected objects" operation in the Object menu. Currently supported

Yes, Boolean operations on shapes are supported. Select the shapes/paths, and use the "Merge selected objects" operation in the Object menu. Currently supported are union, difference, and intersection. The resulting object will be a path. Right now there is no way to change the default white background (exported as transparent), but this would be an easy thing to add.