The "Dynamically Adjust Node Size to Label Size" option works with the rectangular bounding boxes of the shapes. For all other shapes, you will have to adjust the size manually.
The edge connection points can be adjusted in two ways. First you need to select an edge. Then either use the mouse to drag the little black square in the source or target node to the desired connection point or specify explicit source and target port coordinates in the properties view in yEd's lower right corner.