what is the advantage of a dg lens, compared to a conventional lens in terms of image quality on digital slr?

Answer 1

Sigma DG lenses have a smaller image circle than ordinary lenses. For digital SLRs, this makes no difference. DG lenses won't work properly on film cameras, however.
Nikon does the same thing with DX lenses and Canon has an EF lens selection.
The smaller image circle requires less glass, which makes them cheaper to manufacture.