No USB power adapter, just cable 

Yes, this portable carbon monoxide detector has a hole on the top, so we can use lanyard to hang it to the wall 

Yes, but not for long. I is designed to run off AC power and the battery is for backup when you have power outages. You will have a much better experience if you can keep it plugged in. 

You will see data from the outside sensor on your console. Look for rain, wind speed, wind direction, UV strength, temperature etc 

The display console unit can run on batteries only. However, without the a/c power cable, the display only stays on for seven seconds, and to get the display to come on, one has to press a button on the display console. Also, when running on batteries only, the unit will not maintain a wifi connection, so it won't reliably upload weather data to WeatherUnderground or other weather networks.