Add a DragMode that doesn't swap the items but inserts the DraggedItem on the drop position. The XAML team has recently reviewed this request and will not be addressing it as at this time the team is focusing on the requests impacting the highest number of developers. If it is blocking for your work please contact us through the support ticketing system with details on your setup and a reference to this item.
Allow the minimized items to be distributed in rows and columns simultaneously. DECLINED: Duplicated with https://feedback.telerik.com/Project/143/Feedback/Details/114124-tileview-allow-setting-a-number-of-minimized-rows-columns
Add TileViewItem.HeaderBackground property. DECLINED: There is SDK sample available demonstrating how you can change the background color of the header of each item. https://github.com/telerik/xaml-sdk/tree/master/TileView/ChangeHeadersBackground
If a RadTileViewItem hosts several controls (e.g. Buttons, RadioButtons) users should be able to change the focused element using arrow keys.