There could be a couple different reasons why things aren't showing for you, most of the below is going off of the Documentation on the User Contributions, if you haven't checked it out please do!
let's go through the list:
- Is the webpart set up to allow editing by users? You have both an "Allow insert/edit/delete" option that should be true, and also the "Allow editing by users" which you will want to set up properly.
- Do you have a New Item Button label set? i'm not sure if you leave it blank if it won't render one.
- Is the user you are testing with included in the "Allow Users" (IE if it's set to authenticated, are they logged in? If set to Page Owner, are they the page owner?)
- For editing, make sure to add the Edit Contribution webpart to the content template (not the list, but the actual item), as this is how you can allow users to edit an existing article.
Now onto your first question. This is going to require custom coding i'm afraid. You can hook into the BizForm Submit event, or clone and modify the custom registration form and add in the logic to on submit -> Create the page -> use URLRewrite helper class to redirect the user to that page.
For second question, yes it's possible. However for that one, if you just need email notifications, i would instead look to add a custom Global Event Hook. These allow you to "Do something" when certain events occur (such as when a form is submitted, or a new page is created, etc).
For the last question, if you are an Administrator or Global Administrator, you will most likely have access to edit other people's content. The Edit Contribution is to allow non Editors to do this.
Hope that helps!!