The profile is defined as a collection of rules and procedures a person needs to follow to access particular records. There are multiple profiles available in Salesforce. For example, a sales profile can have access to leads, opportunities, contacts, campaigns, etc.
As far as the second question is considered, the answer would be yes. The people who work in one department have the same profile. So the people whoever works under a particular department would be assigned with the same profiles.
As we have seen in the sales profile, many people work under it and every person works under is assigned with the same profile. Hence any number of people can have the same profile.