Learning my own network, inside and out

I think I pretty much know all of the basics to simple networks... But I want to dig deaper, and really understand why something isn't working, and why configurations need to be a certain way, and what certain things mean... If anyone wants to help me understand a few things, using my home network as my example/workspace, that would be great... Here are a few of the questions I have...

How does a piece of my equipment have two seperate IP addresses? For example, my router. Here is the setup, starting from the internet. The internet comes in through the modem. The modem is set to be a DHCP server. The router goes to the modem and gets assigned an IP address by the modem. This IP address is 192.168.254.1. Yet, to my computer, the router is 192.168.1.1? Yet, 192.168.254.1 is still pingable by my computer... So, to that aspect of it, the router is both 192.168.254.1 and 192.168.1.1?

And sort of the same thing regarding the modem and the ISP, correct? To me, the modem is 192.168.254.254, but to the ISP or internet, it's whatever is assigned to it by the ISP?

Is it similar to how, to my computer, my computer is both 192.168.1.whatever is assigned by the router as well as 127.0.0.1?

Also... What exactly is a "bridge"? Is it where two pieces of equipment, say, two different routers, are configured to act as though they are one, in a sense, so that everything connected to them are "one network" rather than two? Or am I getting this wrong?

 

That's what got me confused in the beginning... lol... about the different IP's for the same device. I'll take a look at that website and see if it answers any of my questions. Thanks.

 

Sorta.. lol. I'll probably be taking several computer related classes at the college next semester so I'll get all straightened out then if I'm not able to learn before then. Thanks for the help.