Straight to your questions:
1. You will need to modify the TimeRulerItemTemplateSelector of RadScheduleView, just extract the default one from the used theme and modify HorizontalTimelineMajorItemTemplate
by removing the TextBlock from the template. In order to extract the selector you will need to go to UI for WPF installation folder, then Themes.Implicit folder, drill down to the theme that you're using (the default one is OfficeBlack) and open Telerik.Windows.Controls.ScheduleView.xaml. Then copy the TimeRulerItemTemplateSelector to your application and made the needed changes. All that is left is to apply it to the RadScheduleView instance through its TimeRulerItemTemplateSelector
2. I am not able to reproduce this behavior - in general, when an appointment is dragged and dropped, it stays selected. Could you give us more details on the erroneous behavior you're experiencing?
3. You could modify the AppointmentsSelectionBehavior in order to disable selecting multiple appointments. Please check the following topic for further instructions on this:
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