2. Do Routers Have IP Addresses? If So How Many?

An average home network router has two different IP addresses, one for devices to connect across the LAN (Local Area Network), and one for the internet connection (WAN).

Your router is on the internet, for which is has a unique IP address.

Anything on the inside of your home network is not on the internet, it is
on your LAN, which is a separate local network.
To be part of this network, anything on your LAN must have a unique (within the LAN) IP address. As the LAN is not part of the internet, this IP address can be used by anyone outside the LAN.

There is a third IP address which is shared by all routers: 192.168.1.1, which if you type into your address bar, will allow you to access the settings to your router, and make changes to your home network such as changing your wireless password.

Here's a comprehensive explanation of network devices, that will also provide some insight into the distribution of IP addresses: