How can I see what the proxy Firefox actually uses when I check either of these two options? Does it take it from Internet Explorer? Are they taken from/stored somewhere in the registry?
The settings for use system proxy settings is taken from the internet options (can be accessed via internet explorer or the control panel) and it is indeed saved in the registry. The registry entry is:
Off the top of my head however could be some more settings in there. It also depends on how your proxy is setup from the options.
With the Auto-Detect Proxy settings for this network Firefox and Internet Explorer as far as I'm aware will target a location known as GET http ://wpad/wpad.dat (had to break the link as it cannot contain wpad) which is normally setup when you have a LAN proxy.
This is different to the Automatic proxy configuration URL which is used when you have a Proxy PAC file located somewhere which you have to specify then it will load the file.
It is quite a big topic so anymore information you need I can try to help further just leave a comment.