Straight to your questions:
In order to summarize the duration of the appointment in the current date, you will have to filter them from the AppointmentsSource and calculate it. That is why, I can recommend you to bind this TextBlock, which will display the result directly to your ViewModel. Extending the MonthViewItem will break the logic of the ScheduleView, as it will no be able to recognize it.
Another suggestion is to use SpecialSlots, instead. You could find an example in this online demo
. You could create the style of the slot, so that it can display all the information needed.
Hope this information helps.
the Telerik team