Is it possible to move/resize the task?
This is not currently implemented, but task input and editing functionality is intentionally left open and mostly up to the developer, as workflows and user experience requirements can vary wildly for different users of the plugin.
Other related feature requests, such as #92 and #16, have demonstrated the desire for richer "data interaction" features, though this would require much development work. A built-in way to do what you want without heavy lifting might not come for a while, if ever. In the meantime, however, you can probably use jQuery UI's Draggable widget to implement this for your own needs, and once you get it working, please don't hesitate to make a pull request!
Please make this functionality, this will be very helpful. It is a very nice JQuery plugin but has limited functions. (sad)