There are a variety of chin reduction procedures that can make horizontal and vertical dimensional changes. It would be important to see pictures from both the front and the sides and do some computer imaging to see exactly the type of chin reduction changes you desire. A chin reduction can be done is such a way to make it more square if desired.
yes, you could modify the height and the prominence along with the contour of the chin. In the final analysis, the chin has to be viewed alongside the overall facial proportions and jawline.
The answer is yes. The benefit of sliding genioplasty is that you can move the chin any where you want. So in this case, it would be up. I would avoid shaving.
Yes it is possible. But before proceeding with chin reduction I would recommend a thorough analysis of your facial proportions the relationship between your upper and lower jaws and teeth.