Hide webform after the user's first submission
After creating your webform, go to the "Form Settings" under "Webform". In case you don't find it, here's the URL: node/Nid/webform/configure (I choose not to remind you of the Nid that you should change :)). 

Here, you should see an option for "Per User Submission Limit"-
In your scenario, Limit each user to "1" submission(s) "ever".