Q: Cinema display behaves differently than Thunderbolt display?

I used to have a MacBook Pro with a Thunderboly display but I sold and bought a Mac Pro with a 24" Cinema Display. Since then, I have had an assortment of "issues" but for all I know they may as well be features of the cinema display.

1) The 3-finger swipe only moves 1 desktop, whereas it used to move both desktops on my Thunderbolt setup.
2) Can't get rid of the menu bar when watching fullscreen videos on YouTube or in VLC.
3) Lost the ability to "drag" a window from one desktop to another.

Any ideas?