S3 doesn't have the notion of folders commonly found in file systems but instead has a flat structure, more details can be found here.
Instead, the full path of an object is stored in its Key (filename). For example, an object can be stored in Amazon S3 with a Key of files/2020-12/data.txt regardless of the existence of files and 2020-12 directories (they are not really directories but zero-length objects).
In your case, to solve both points you are mentioning, you should leverage S3 event notifications and use them as a Lambda Trigger. When the Lambda function is triggered, it is passed the name of the object (Key) as an argument, at that point you can simply change its Key.
I.e. Object is uploaded in s3://my_bucket/uploads/file.txt, this creates an event notification that triggers a Lambda function. The functions gets the object and re-uploads it to s3://my_bucket/files/dec/file.txt (and deletes the original one).