Is there any way to let windows control their borders and decorations?
Yes you can, but since you are insterested in designing you should try searching how to make it, with simple google i found that this is good.
Part of the security design of Qubes is that only dom0 controls trusted window borders. If another qube could control its own borders, an untrusted qube could masquerade as a trusted qube and trick you into entering sensitive information, like passphrases.
More details: Getting started | Qubes OS
I thought this might be the case. What about dragging windows: In Firefox, the windows can normally be dragged by the tab bar, in Qubes they cannot. Is there any way to work around this?
Drag the title bar.
It’s a peculiarity(?) that the Drag options are missing from Customise
You mean Qube’s customize options?
That’s odd. Dragging by tabs in Chrome works just fine. Possibly a Firefox bug?
I don’t mean dragging the tabs, I mean dragging the empty tab bar space to move the window. Might not be easy to change.
Doesn’t sound like a convenient feature to me… Try to hold
alt and drag from any place of the window.
This option (and the settings in Firefox customization, are being
removed in recent builds, so we are ahead of the game.
Alt+anywhere are reasonable alternatives.