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While it makes it easier if you have an actual domain infrastructure, all you really need for the SSL to work correctly is a functional DNS that translates the Fully Qualified Domain Name (FQDN) to a computer's IP address.
If your server needs to be available from outside the network using that FQDN then DNS management is a bit harder. You will need to consult with a networking guy that knows his DNS. Best to pick someone locally that can come on site.
Ditto. You can have your own Domain Name Server. Get help if you need it.