I`m having trouble with a project. One requirement of the project is to be able to access both the VNC server and proxy server through a domain name.

As far as I know, I have to simply type in the ip address of the VNC server to access it.

I do not have a DNS server to test but if I want to access the VNC server through the use of a domain name(example "www.plmqaz.com"), do I simply type in the domain name and port number to access the VNC server?

If so, is this the same with Squid Proxy? Do I simply have to type in "www.plmqaz.com" in the Firefox proxy connection settings with the port number to enable the machine to use Squid?

If not, how should I go about doing it?

yes. What you're asking about has absolutely nothing at all to do with squid / vnc, that's just DNS.