A. A. The basic answer would be Yes, however it is advisable to use one of the following ranges which are reserved for use by private networks:
10.0.0.0 - 10.255.255.255 this is a single class A network
172.16.0.0 - 172.31.255.255 this is a group of 16 contiguous class B networks
192.168.0.0 - 192.168.255.255 this is a contiguous group of 256 class C networks
The addresses above are detailed in RFC 1918 (Request for comment). Obviously if you did one day want to part of your network on the internet you would need to apply for a range of IP addresses (from Internic or from your ISP).
These addresses are routable and routers will route them by default. You aren't supposed to route them publicly, and need to configure your router accordingly. Internet backbone routers have been specifically configured to not route these addresses, but that is a specific configuration choice.
People using these addresses must specifically configure their routers to not route these addresses. Routers route these addresses by default as they don't know whether they are gateway routers or some intermediate router on a WAN (behind a gateway). Obviously if you're using them internally you want your Intranet routers to route the addresses or you won't be able to communicate inter-subnet.