The network address is NOT the router's address. The router is using an IP address from one of the host addresses in the subnet. For example, if you have a subnet of eight IP addresses (0 - 7), 0 will be the network address and 7 will be the broadcast address. The router may use one of the IP addresses from in between these two [1 - 6]. As another example, look at the picture below. Each of the router's interfaces(underlined in red) is using an IP address from one of the host IP addresses in the respective subnet.

Answering your second question, the address you provided is from the CIDR notation. CIDR stands for Classless Inter-Domain Routing. CIDR addresses do not have classes. They replace the previous classful IP addresses, which to my knowledge aren't used anymore.