Seems you will be attempting to build a complex network environment without the proper knowledge - may I suggest hiring network professionals with proper background/education to build it correctly, or at least in advisory capacity?
To answer some of your specific questions:
DNS servers are used to translate domains/hostnames to IP adresses, yes.
DHCP servers lease out dynamic IP addresses to clients.
Both those types of servers (and other types, i.e. DC, etc.) can be on the same physical machine, they are software packages. DHCP is often off-sourced to some type of appliance, like a firewall or a NAT router. In other words, a DHCP server can be a function of your NAT router, of your Firewall, of your DC, of any server, etc. It is up to how the network is set.
Properly configuring a DNS server, a domain controller, file servers, etc. in a large campus area network is not trivial, it cannot be accomplished by simply buying a separate "server" computer preconfigured for each task.
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