Eliminating the shadows? Easy, don't stand between the light and the subject. I know that might sound a little sarcastic, but that's really all there is to it. When you put something between a light source and a bacground (subject), you get a shadow.
The first image looks very flat to me; despite the long shadows, I suspect the sun was still too high in the sky. Ideally early morning and later afternoon/evening are the best times for [most] outdoor photography, with the light becoming less "attractive" closer to noon. The image is also at least 1/2 stop over-exposed.
Notice as well that the image isn't straight; the "Stop ahead" sign is on a definite lean. Always try and make sure your camera is level, even if it means getting into an awkward position. I would suggest trying to redo this image so that you have all of the child in the frame (not cropped at the knees) and using a much shallower DoF to 'blur' the background.
As far as #2 goes, it's slightly over-exposed, but not so much as the first. Always try and have the subject looking toward you; not always right into the camera, but at least toward you. This is one of the difficulties of photographing young children. They often tend to do their own thing. This image also needs to be straightened.
Just my $00.02 worth - your milage may vary.
~John