I am glad to hear that you are using our Calendar control for Xamarin.iOS.
Let me get straight to your questions:
1) Deselect the Selected Date:
The TKCalendar control does not provide this functionality out of the box. In order to deselect the selected date you could use a button. On its TouchUpInside event set the SelectedDate = null.
2) TKCalendar SelectionMode.Range:
Regarding to the range selection mode you could check the following article in our native documentation: Calendar: Selection.
Also you can take a look at our native developer focused examples for Xamarin.iOS. For more information please refer to the following article from our documentation: Developer Focused Examples.
Please review the attached project how the deselection and selectionmode - range are implemented and let me know if you have any additional questions.
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