When 2 objects are grouped together, magnetism doesn't work, is there a way?

Select them individually in the group by clicking a second time on one of the objects of the group then selecting the second one by clicking on it with shift key pressed. You may also select them in the furniture list.

Automatic side-by-side alignment doesn't work on all sides.

Side by side alignment aligns the second and following objects of the selection on the back of the first selected object (opposite side of the thicker line of its selection rectangle), without rotating them. So pay attention to which object is first selected.