The “correct” IP and DNS addresses on a LAN are what ever the network administrator set up. They could be anything.
I don’t know what you mean by “Administrator IP”. I think you mean default gateway IP.
On a Unix box you can look at /etc/resolv.conf to determine the DNS servers being used by your machine. You can do a “ip addr list” command on a Linux box to see what your IP address assignments are.
On a Macintosh you can look at the network preference panel to see the network assignments you have received.
Since you mention Internet Explorer, I assume you are on some flavor of Windows. And that is an OS I don’t use enough to be able to help you on. I expect that there will be a control panel somewhere for networking that should tell you what you are asking but I don’t know enough to tell you where to look.