Cannot dynamically change the theme of the control.

PanelBar: A custom template can not be set to a PanelBarItem, using a ControlTemplate

DECLINED: This issue is not reproducible with 2016 R3 official release.

Items to automatically adjust position when PanelBar has no scrollbar. See attached project.

DECLINED: AdjustPositionOfPanelBarItemsNoScrollBar SDK sample demonstrates an approach to customizing the RadPanelBarItems to include a ScrollBar when the RadPanelBar's vertical ScrollBar is Disabled.
https://github.com/telerik/xaml-sdk/tree/master/PanelBar/AdjustPositionOfPanelBarItemsNoScrollBar

Make expand animation to be horizontal when Orientation is Horizontal.

DECLINED: Cannot reproduce with R3 2016 binaries.

Second level items cannot be styled to look like first level items.

DECLINED: SecondLevelItemsStyledLikeTopLevelItems SDK sample showing approach to styling PanelBar with more than two levels of PanelBarItems is available since R3 2016 Official Release.
https://github.com/telerik/xaml-sdk/tree/master/PanelBar

Add an Icon property to allow displaying images in the RadPanelBarItem Header.

Declined:

Adding such property requires also adding a visual element (Image) in the Template of the RadPanelBarItems.
RadTreeView also has Image in its ControlTemplate and we have to admit this was our design mistake in the past. Such element makes the Style larger, makes the virtualization harder to support, slows down the performance.

How To Add Image in RadPanelBar:

In non-databound scenarios just add the Image in the Header:

      <telerik:RadPanelBarItem>
                <telerik:RadPanelBarItem.Header>
                    <StackPanel>
                        <Image Source="MyImage.png" Margin="5"/>
                        <TextBlock Text="{Binding Name}" />
                    </StackPanel>
                </telerik:RadPanelBarItem.Header>
            </telerik:RadPanelBarItem>

In databound scenario set the ItemTemplate of the RadPanelBar:

DataTemplate x:Key="itemTemplate">
                <StackPanel>
                    <Image Source="MyImage.png" Margin="5"/>
                    <TextBlock Text="{Binding Name}" />
                </StackPanel>
            </DataTemplate>

 <telerik:RadPanelBar ItemTemplate="{StaticResource itemTemplate}"/>

See the SDK example demonstrating those approaches: https://github.com/telerik/xaml-sdk/tree/master/PanelBar/AddHeaderIcon

Now if you add a content to the panelbar the content inside will receive tab navigation only once due to the items control nature of the control.

The XAML team has recently reviewed the status of this issue and won't be addressing it in future releases.
In order to make the content (items) of a specific RadPanelBarItem (X)  focusable with tabKey, set TabNavigation="Local" on X.