> Edit: Also would it be possible for applications to enter into full screen mode?
No. If they could, then when they were told to full screen (or do so "automatically"), they could draw as convincingly as possible a Qubes-looking desktop and trick users into thinking it's their own desktop, allowing them to phish credentials and whatnot. The viability of this attack is low, but it can be avoided by not allowing full screen.
(Edit: Apparently I was wrong. It is possible to enable fullscreen manually, according to a sibling comment.)
I have few usability related questions to see if such things would be possible in Qubes OS.
Would it be possible for Qubes OS to implement similar window maximization as one can see in Ubuntu?
That is, when a window is maximized then its title bar integrates with the toolbar.
Edit: Also would it be possible for applications to enter into full screen mode?