Ok, just a few in order here...
1) Yes, you can change the background image for your dot view by selecting "theme" in the dot view setup settings...
2) You can only activate Cortana when the screen is OFF... She won't come up if the screen is on...
3) This was a bit embarrassing when it happened to me, but the "Cortana not responding" thing was something silly for me. First make sure you ask her a normal thing that she would respond to... "Cortana, tell me a joke." is a great one to try out. If she doesn't respond, open the device, turn up the media volume and try again... Worked wonders for me - and stop laughing at me now...
Anyone have any other questions?