I would like to know if WriteBackExtreme keeps a log of who adds data and when the data was added.
Yes! An '_audits' table is created in your repository database which stores the history of each data point that's been added using WriteBackExtreme. Users are stored, the time too as well as the information of what was added to which table.
A great feature of WriteBackExtreme is the history mode, on the front end you can see the history of all posts that have been added to that schema.