I have a custom WindowChrome style for my WPF app (ripped from here: http://www.bdevuyst.com/wpf-custom-title-bar-and-taskbar/).
Code here:
It is your command bindings that are the issue here. Don't bind the Command properties. Simply set them:
You will also need a command binding for each of the commands and execute them programmatically as suggested by @Louis Kottmann here:
In WPF, can I have a borderless window that has regular minimize, maximise and close buttons?