Steven Zahm@ Robert
re: I want to know if members can login and edit their own listing?
It is the Link extension. This extension will allow registered user create and maintain their entry. If an entry already exists and the user logs in with a email address matching an entry, that entry will be linked their user account which will allow that user to maintain that entry even if they change the email address in the entry or their user account. This is possible because once a link is made, it is persistent.
The other extension you might be interested in is the Form extension. This will add frontend editing for both the site admin and users linked to entries by the Link extension.
Hope that answers your questions thoroughly!
ps. Here are the docs for those two extensions to help you get started.