Can chess players agree to manipulate the results? Take the following scenario, which may happen in tournaments that's why I'm asking my question:

A famous old GM who's not playing well plays against some teenager who's very strong, The GM will be embarrassed to lose against some teenager, the GM has a lot of money, the teenager needs money for college. So the  GM pays the teenager so he could win.

Or maybe could they manipulate results by mutual agreement, like what happened to Algeria in the world cup 1982. Could they agree to eliminate an opponent? What the rules has to say?

I know it's against the rules, i just want to know how they investigate it and what are the rules about it, and yes i'm also asking about draws, since manipulating the results isn't only about winning and losing.

And I'm also interested in knowing if the officials can deny a draw, if they see that the game is still playable or if they see something suspicious about it. And could you draw at any stage of the game: like d3 e5 and they agree to draw here, is it possible?
In a nutshell, current rules allow pretty much any sort of "spontaneous" agreement to a draw at the board, even if one side is staring at a forced mate in 6. If money changes hands or the results were agreed to before sitting down to play, it's a violation of the rules, but it's hard to enforce because folks who do that do it without witnesses to the act.

The "Sofia Rules" are an attempt to combat that, we'll see how long they last and whether they get applied to more than a few top tournaments.

If an official has evidence, he can declare a game forfeit, but that is subject to appeals where the evidence must be presented. If an official becomes known for doing it capriciously, no one comes to play; if a player gets the reputation for "selling points" he is often invited to play in tournaments where the goal is to get one or more players some title norms. So you can see the field is tilted in favor of the players. Not saying that's good or bad, just saying it is.