Question

How did buddhism affect existing laws or culture

Answer 1

If that is about South Asia there were major affects on almost every field of life by Buddhism. For example Hinduism was the prevalent religion in the area before the Buddhism which had a strong social system based on various classes; Buddhism denied all of that bringing in more people from low casts (who were considered low cast by previous cultures). This also brought about a whole transformation in the society.
Buddhism also preached "Ahinsa", meaning non-violence (though there have been clashes but the primary teaching was of non-violence) which affected some parts of Western society as well. Buddhist architect and art is a whole new chapter in the history of South Asia also.