Is there a way to remove black border around the elements? It seems to be automatically added by sweethome3D.

No, and there won't. This rectangle is used to show the user in which zone he can click to select an object, but it's not printed or exported to PDF / SVG.

Any idea about automatically rotating the icons depending on the base?

I don't understand what you want. Why don't you use the rotate indicator available on each object?