Allow users to edit own unpublished content
I am not sure about your exact requirement. If you want to list all contents created by current user with an edit link, my suggestion to make try with views.


Give Edit Own Content permission to your needed roles for all content types in Home » Administration » People » Permissions.
Create a view with content of all.
Add title in fields (or the fields you want).
If you want to give an edit link , add Content:Edit Link.
In views contextual filter add Content:Author uid = User ID from logged in user (Refer here).
Change format to Table (Only title and edit link is there this gives a nice formatting).


Hope this will help you.