That would be called a server. A server "serves" the computer files or printer access over the network for client computers access.
There are multiple connection options for a Network Printer. 1. The Printer can be attached to a Router and be available to all of the Network's Computers that can access that router. 2. If the printer is attached to Computer "A" (via USB or WiFi) any Computer on the Network that can access Computer "A" can be allowed to access the Printer. Of course Computer "A" MUST be up and running.
If the printer can connect to the wireless access point via ethernet and that the printer has been enabled to be used on a wireless network then in theory yes.
The role of ethernet switches in a network is to allow computers and other devices to talk to each other. This also allows many users to access a shared device such as a printer.
Servers
It depends on the printer you have. But basic instructions are to log into the default IP Address of your home network's router /modem. put the IP address into your printer and have the network access key.
Generally taken, in computer technology, to be 'Local Area Network' - for example the network of computers connected to a central device (server, printer, router etc.) which all can use or access.
proxy or firewall
If we need to allow personal computers to participate in computer network and shared file and printer access within a local area network (LAN). At that time after physically connecting the server computer to the network, we can install the network operating system (NOS) on the server.
After sharing the printer, add the users or groups that you want to have access to the printer, along with 'print' ability, such as 'create document' authority.
File servers do those things. There are specialized servers as well, for example web servers, database servers, remote access servers, fax servers--the list goes on and on. But file servers are the backbone of providing access and managing files and who has access to what resources at which times.BTW. Access to the network is usually referred to as Authentication. And Rights or Security Management is usually what controls access to files, printers, and other resources.
Network Access point
there is no limit of computers.. it depends on the local access network network's strength, capability.