Does DayPilot use ASP.NET Ajax?
No. DayPilot uses only tools available in raw ASP.NET 2.0 (Callbacks). But DayPilot is compatible with ASP.NET AJAX (UpdatePanel in particular) so you can use it together.
Does DayPilot use its own Ajax framework?
There is some AJAX-related plumbing but 95% of the code is application specific (calendar-related) so there is minimum overhead.
Does DayPilot uses some parts of AjaxControlToolkit?
No. AjaxControlToolkit is included in the DemoSQL to demonstrate invoking a modal popup using ModalPopupExtender but this is just another demo.