The proper netmask for an alias IP address

The only thing is that you're not saying "all addresses should have access" -- that's done in your firewall(s) and/or the server software and/or other security layers like tcpwrappers.

0.0.0.0, in this context, means "all IP addresses on the local machine" (in fact probably, "all IPv4 addresses on the local machine"). So, if your webserver machine has two IP addresses, 192.168.1.1 and 10.1.2.1, and you allow a webserver daemon like apache to listen on 0.0.0.0, it will be reachable at both of those IP addresses. But only to what can contact those IP addresses and the web port(s).

Note that, in a different context (routing) 0.0.0.0 usually means the default route (the route to "the rest of" the internet, aside from routes in your local network etc.).

A UNIX socket, AKA Unix Domain Socket, is an inter-process communication mechanism that allows bidirectional data exchange between processes running on the same machine.

IP sockets (especially TCP/IP sockets) are a mechanism allowing communication between processes over the network. In some cases, you can use TCP/IP sockets to talk with processes running on the same computer (by using the loopback interface).

UNIX domain sockets know that they’re executing on the same system, so they can avoid some checks and operations (like routing); which makes them faster and lighter than IP sockets. So if you plan to communicate with processes on the same host, this is a better option than IP sockets.

Edit: As per Nils Toedtmann's comment: UNIX domain sockets are subject to file system permissions, while TCP sockets can be controlled only on the packet filter level.