Expose a property through which the TabContentPopup IsOpen state can be programatically controlled. This feature should allow the implementation of a scenario where the TabContentPopup is opened when hovering over the tab.

Declined: The current API of the RadRibbonView allow the users to control MinimizedPopup. A sample application is attached demonstrating how the Popup can me controlled

The MinimizedPopup could be open/closed by using the SelectedIndex property of the RadRibbonView.

A sample implementation could be seen in the attached project.

Add panel element to the TabStripAdditionalContent property. This way it will be easier for the users to add content.

Declined: The existing API for the TabStripAdditionalContent property (of type Object) easily allows the users to customize and insert content depending on their requirements. For instance if you want to use data from ViewModel and list all of its Items you could use the following code:
<telerik:RadRibbonView.TabStripAdditionalContent>
	<ItemsControl ItemsSource="{}" >
		<ItemsControl.ItemsPanel>
			<ItemsPanelTemplate>
				<StackPanel Orientation="Horizontal" />
			</ItemsPanelTemplate>
		</ItemsControl.ItemsPanel>
	</ItemsControl>
</telerik:RadRibbonView.TabStripAdditionalContent>

ApplicationMenu do not have keyboard navigation - pressing arrows do not navigate thru the application menu items.
Declined as a duplicate of: https://feedback.telerik.com/wpf/1352753-ribbonview-applicationmenu-do-not-have-keyboard-navigation.

Currently, Title and Description properties are typed to string and the control template uses TextBlock controls to display these properties, I think that only typing these properties to "object", showing them with  ContentPresenters and adding a pair of DataTemplate Dependency properties (TitleTemplate and DescriptionTemplate) would offer an extremely flexibility to this useful control.

Declined: If the users need to transfer object data to the ScreenTip they could use the Tag property(http://msdn.microsoft.com/en-us/library/system.windows.frameworkelement.tag%28v=vs.110%29.aspx)  and bind its value to an custom Implicit style targeting the ScreenTip. 

Add MouseOver Selection states in the RadRibbonTab control

Decline reason: RibbonView and its elements (including TabControl) are inspired by MS Office products. Since hovering over the selected TabItem in MS Word for example doesn't change its visual appearance it shouldn't in RibbonView as well.
If your project design still requires such appearance then we highly recommend that you edit the Control Template of the TabControl in Telerik.Windows.Controls.RibbonView assembly and add a MultiTrigger Condition (in WPF):
  <MultiTrigger>
                <MultiTrigger.Conditions>
                    <Condition Property="IsMouseOver" Value="True"/>
                    <Condition Property="IsSelected" Value="True"/>
                </MultiTrigger.Conditions>
...
</MultiTrigger>
or add a  <VisualState x:Name="SelectedMouseOver"> to CommonStates VisualStateGroup.