Is it possible to have a form built by a user?
For this you would have some kind of editor that would create a html string. This string would be stored into your database and then upon request you would display it on the user's site.
The editor should be very strict into what it can add and what the user has control over, there are some javascript editors available that will be able to provide this functionality.
The only issue I can think of is that you may run into django escaping the form when displayed to the page.
For example:
I have a user that wants to create a contact form for their personal website. They want three input type=text and one textarea and they specify a label and an name/id for them on my site. Then they can use this form on their site, but I will handle it on mine? 
Is it possible for django to spit out custom forms specified by the user?
Edit: If django is too "locked down" what would you recommend I do? I would like to stay with python.