-Every camera can blur the background. That's called depth of field. The shallower it is, the blurier the bacground is. So you need the cameras (or it's lenses) F number be as small as it's possible. 1 is the best.
-The first 3 options can't be done by a camera, so you have to use a computer do to this. The best video editing Program is Adobe Premiere Pro, or Sony Vegas.
-A stand can be bought separately.
-Great sound can be earned by an external microphone
-Beautiful photo and video quality by a large sensor, and large resolution.
I don't know how much money can you spend on a video gear, but here's mine:
-Canon EOS M + EF-M 18-55mm IS STM + 90EX + EF-M 22 f/2
-Hama Profil Duo II Stand
-Asus K72JR Laptop (2,53GhZ CPU and 8 gigs of RAM) - Adobe After FX and Sony Vegas 11.0 installed
That's all, you can buy a PC, so you have to spend less money on it. I Hope I could help you, have a nice day!