Gravity Forms will work to capture the information on one site and create one post. You can use a plugin like FeedWordPress to populate content on your other sites:
Or, you could write custom code to post with XML-RPC to post remotely to your other three sites. Gravity Forms has a gform_after_submission hook which could be used to create posts on other sites after your form is submitted. http://www.gravityhelp.com/documentation/page/Gform_after_submission
Regarding comment 2, there is no specific integration with any plugin to create events. Some events plugins use custom posts to store event details and since Gravity Forms can create posts, including posts of custom post types, you can create a custom post which matches the format of the custom post created by the event or calendar plugin.
Here is an events plugin which uses custom post types:
Posted 9 years ago on Saturday October 27, 2012 | Permalink