A default gateway ip address must always be the 1st usable ip address of a network? If the 1st usable ip address range is not used could it work?

No with out  default gateway ip address we can use internet .but we can managed to used with a gateway  although it is very first or last end ip that we have configured for our dhcp router 

No, the default gateway doesn't have to be the first usable IP in a network. But when you choose another IP, make sure that no other device will conflict with it. For example, reserve the gateway's IP in DHCP.

Basically The default gateway IP is Router IP if u set any other ip Address instead of 1st or second you just have to select the IP for Router its is the door to take u outside