The problem with your original sentence is that you used "which" to refer to people. "Which" only applies to things, so we say "who" to refer to people. In this case, you could use "whom," since it's the object of the verb (the subject is "society"). Personally, I wouldn't use "whom" except in a really formal written context. Another option would be to introduce the relative clause with "that" -- this is only an option when the relative clause in defining (i.e. restrictive), as it is in our example. Some people would say it is preferable to use "that" when possible, since it highlights the fact that our relative clause in defining. A third option, since the relative clause is defining and "that" is the object, would be to omit the relative pronoun entirely, which actually sounds very nice:

"Just because you know certain people who(m) society wants to know,...."

"Just because you know certain people that society wants to know,...."

"Just because you know certain people society wants to know,...."

As far as "society" being singular or plural, in US English, it's always singular -- this is known as "formal agreement" -- the word is singular in form. In UK English, they often use "notional agreement," so your friend's usage is probably correct in British English (although even the British sometimes use formal agreement when they want to emphasize everyone working together as a unit).

I talked to my English teacher and yes he said the same thing about the usage of "which" 

But he said my friend was wrong in this case about the usage of "people of society" because my sentence was directed to all the people. 

The usage of "people of society" is used to target a certain group of people. Like people of society who are into drugs. Which wasn't in this case as my sentence was targeted towards all types of people. 

But anyways thanks Phil for taking time to correct my mistakes :)