So you are wanting to know if you can run it on your laptop and if you can connect it to your xbox 360?
First, while the device can be connected to an external monitor, your laptop is technically not an external monitor. Lap tops are really not made that way. Where you can take an external monitor and add it to a laptop, you really can't use (as far as I am finding) the laptop as the external monitor. However, since this would fall under the laptop settings as well, should you wish to try, I would check in the "Laptop Tech Support" forum ...
http/www.tomsguide.com/forum/forum-111.html ... to see if they think it is possible.
Now if you just wanted to attach an external monitor, that you could do. However, The Micro HDMI socket on the Yoga2 Pro is too recessed, so many connectors just don't connect at all or give flaky connections that drop out with any vibration / touch to the cable. Due to this, it can be hard to find a connector cable that will work.
In regard to connecting to an x-box, I find nothing about connecting to an x-box itself. There is info out there on connecting an x-box controller to your tablet, but that is all I can find.
It sounds a lot like you are wanting to do things with it that it may not be truly designed for. I would suggest contacting Lenovo directly and see if they can assist you with the connections you wish to make.