What things should we know about the company's product/ service, in order to deliver a good customer service?

It's everything about the service/ product plus the company operating procedure. An ideal customer service unit knows well to handle customer queries and complaints. It should be able to communicate well info its customers should know, and these are delivered in the simplest terms...never too technical nor complicated to understand.

good listening, with a good assumption of responsibility of the customer

We should know everything about the product or service as to deliver the service quality the customers deserve.