S3: possible for a website user to delete content in S3?

This can be achieved using Cognito and the Javascript AWS SDK so that the user can assume a role and delete content on S3 (as long as the Cognito role the user assume permits). It is , however, possible that they will need application logic that would need to reside server-side (e.g. if a user removes content, a set of actions need also to be performed, or perhaps the rights provided to the user needs more logic). In that case, they could put that logic in API Gateway.