Is it possible in SAP that when documents are created the owner is automatically selected based on the user that is logged in?<br/>
Also is there a log to see what user did what and when?<br/>
You can assign a formatted search query to the owner field. The query you should use to retrieve the current user is:
Select T0.u_name from OUSR T0 where T0.internal_k = $[USER]
The change log can be viewed from the tools menu>change log.