How can I style the border and title bar of a window in WPF?

Those are "non-client" areas and are controlled by Windows. Here is the MSDN docs on the subject (the pertinent info is at the top).

Basically, you set your Window's WindowStyle="None", then build your own window interface. (similar question on SO)

You need to set

WindowStyle="None", AllowsTransparency="True" and optionally ResizeMode="NoResize"
and then set the Style property of the window to your custom window style, where you design the appearance of the window (title bar, buttons, border) to anything you want and display the window contents in a ContentPresenter.

This seems to be a good article on how you can achieve this, but there are many other articles on the internet.