Create webform on node insert?
Under /admin/config/content/webform you can enable your event content type for webforms, and the form will be created as part of the node creation process.

Edit: Misunderstood! 

Webforms are one-off forms. If I now understand correctly, you want to re-use a standard form on each event page (only one form created). 

To do this, create a webform with the required fields, and while editing the form, go to the webform tab > Form Settings. Under Advanced Settings at the bottom select 'Available as Block'.

You can then use the Block settings to display the form on every Event page as required.