My internet connections works well, but where can i find it's configuration files?
I tried to find it here:
but, there is nothing relevant to my eth0 connection.
Since you mentioned that you are using the GUI, I thought I'd show you how to do this through Unity.
When you use Unity, the networking stuff is handled by Network Manager. There is a GUI method to access the connection details.
(1) Click on the connection icon on the top bar. It may look like a plug, or parallel arrows, if you're using Ethernet and not Wifi. Left click it.
(2) Then, you click "Connection Information".
(3) When you click that, a window with connection information will show up. It will look similar to this. Note that I'm on WiFi so the information you have MAY NOT MATCH exactly.
This will contain information INCLUDING the DNS servers used, the IP your computer has (NOTE: This will be whatever DHCP/ISP/Source of the IP address sets, not necessarily your public IP.), and other information.
You did mention that you wanted to tell if it's DHCP or static. Unfortunately, unless you know how your network is set up, you can't easily tell whether the IP your computer receives is static or dynamic or DHCP-assigned.