I know I can move files by renaming them in wdired mode. I am wondering if there is a chance of creating, copying, deleting files/directories in writable dired mode.
No. C-h m in Wdired mode tells you this, among other things:
In WDired mode, you can edit the names of the files in the buffer, the target of the links, and the permission bits of the files.
and this:
The only editable texts in a WDired buffer are filenames, symbolic link targets, and filenames permission.
Just use C-x C-q to toggle back to regular Dired mode, where you can easily create, copy, and delete files and directories.