I have an application using the Graph API. I have it creating events for the user, but would like to let the user invite their friends from our site instead of having to go
see Inviting selected users to Facebook-Event (via Graph API)
Facebook now has a graph api for inviting friends to events.
http://developers.facebook.com/docs/reference/api/event/
invited
Create
You can invite users to an event by issuing an HTTP POST to /EVENT_ID/invited/USER_ID. You can invite multiple users by issuing an HTTP POST to /EVENT_ID/invited?users=USER_ID1,USER_ID2,USER_ID3. Both of these require the create_event permission and return true if the invite is successful.
And the answer to your side question is here: Attach image to Facebook event (php sdk, rest or graph api)