If I go Settings → Network → Wireless and select Use as Hotspot..., I get the following message:
If you have a connection to the Internet other than wireless, you can use it to share your internet connection with others.
Switching on the wireless hotspot will disconnect you from ABC.
It is not possible to access the internet through your wireless while the hotspot is active.
What are the technical reasons why I can't set up an Hotspot and be connected to the Internet at the same time?
You're basically after turning your PC into a WiFi repeater.
If you use Ubuntu, you can use create_ap to create a hotspot:
sudo create_ap wlan0 wlan0 SomeNetwork SomePassword
Where the first interface is the device you want to use for the hotspot, and the second interface is the one that has access to the internet. Since you're repeating over the same adapter in your case, use the same interface.
If you use Windows, you can use Connectify Me or any similar software to use the same adapter that connects to the internet to run a hotspot.
