The word "people" is used as both singular and plural. This is used when speaking in general terms. For example: "There are a lot of people here at the mall today." "Peoples", however, is used when referring to multiple groups of people or cultures. For example: "There are many unique traditions held by the indigenous peoples of the Americas." Another example of this is the word "fish". "Fish" can be either singular or plural. When referring to many schools of different types of fish, however, one can say "fishes". Kind of confusing, but don't worry, "peoples" isn't used all too often, except for in more formal writings. I hope this helps! :)

Oeople is the usual plural. Peoples has a very specialized use only-- when we are speaking ethhnographically of various races, tribes, populations, etc: The peoples of South America include the Jivaro, the Wayana and the Inca.

You're talking about nouns that can be countable or non-countable, depending on context. There are a lot of these. "Cheese" is another that comes to mind. (You can tell how my mind works.)