How can you tell if you have a cavity on a x ray, and can dental x rays cause shadows on a tooth, if it is not done right?

Looks dark. Viewing dental x-rays, we look for darkness on film meaning less dense tooth. In between teeth, we look for a break in the enamel shell. We also look for other abnormalities on these films including bone loss, radiolucencies in jaw bone, impacted teeth, etc. It would be difficult to alter specific locations on films. The film would be too dark or light. So, no.
Shadows. The reading of radiographic images is an art and science that requires some training. X-ray images are tools to help us identify pathology. Areas on the teeth that show up dark can be indications of dental decay. But you must distinguish between natural structural shadows and diseased carious lesions. That is what your dentist helps identify when he reads those radiographic images.