In most cases these are games you don't play to win. Players cooperate, trying to succeed as a group. (Paranoia would be a counterexample here -- characters have a common goal on the face of it, but spend most of their time sabotaging one another. Of course the players still have the common goal of enjoying their characters' backstabbery.)
The GM can play favourites, but this usually simply takes the shape of rewarding players who play 'well', whatever that means in the context of the specific game and group. It's pointless to do this in secret, since it's meant to be a gentle encouragement to the other players to shape up.
Oh man ... "no rules"? Different systems vary a lot in terms of rules volume, but you can go to very simulationist extremes. Of course each group will find the level of rule-basedness versus story-priority they're comfortable with -- as with every (non-computerised) game, players can always agree to change or not to use a rule they don't like.
Story to adhere to ... varies again. A very confident and experienced GM may take the game into the direction of improv theatre and really make everything up as required; but most GMs prepare. They have a story to tell, and players will broadly cooperate in taking the story where the GM needs it to go, simply because the current storyline tends to be the most interesting thing available to them in the game world. A GM may have made up their own plot, but you can also buy ready-mades, the system-specific ones of which are often published by the companies who also make the rulebooks.
True, but only because most rulesets would need a REALLY HUGE box cover to fit into. Roleplayers have rule books. Of course, arguing about rules gets in the way of the collaborative storytelling and is officially Not Fun, so people who overdo it may find themselves getting punished by fate (i.e. the GM).