Can you use the network IP address as a host address?

I'm somewhat familiar with RFC 3021 (use of /31 for point to point links). I get why the broadcast IP address can't (shouldn't) be used as a host IP.

What is the purpose of not using the network IP address (let's say IP address 192.168.0.0 for 192.168.0.0/24)? If I set my host IP to that IP, would that not work?

What is the purpose of the network IP address? I was thinking it might have something to do with the routing table and routers storing the network IP address, but given any IP address and a netmask, the router should be able to determine the network.

I've tried pinging my network IP address, and got interesting results. Seems my default gw responds, but also another device responds, resulting in (DUP!) packet messages.

The reason this has come up is that I'm trying to figure out why I can't access a new IP from a new location. I was given an IP from the provider. Though I can't ping that IP (confirmed default routes are set), I'm able to ping the network IP, gateway, and broadcast IP over the internet, which I thought was strange.

Thanks.