Is there a reason why my legs shakes sometimes when I walk down stairs? I've also noticed that I have a slight shaking in my hand when holding a spoon

See your doctor. It is not possible to diagnose anything on this basis, benign essential tremor, parkinson's disease and simple fatigue are some of the possibilities.
Mutiple reasons. A tremor is an involuntary, somewhat rhythmic, muscle contraction and relaxation involving to-and-fro movements of one or more body parts. It is the most common of all involuntary movements and can affect the hands, arms, eyes, face, head, vocal folds, trunk, and legs. Most tremors occur in the hands. In some people, tremor is a symptom of another neurological disorder. Thank you, check it out.