And question no. 2: would there be a sort of monetary system in an anarchist society? I believe not, since I read many times on this forum that in anarchy everything would be free for everyone; but then what prevents me into becoming an absolute parasite for the society?
Well, there's hundreds of theories on motivation, actually motivation is an entire field of psychology, and secondary motivators like money are only a small part of it, so I'm not really qualified to know exactly what will prevent you from being a parasite. I will say though that there is a growing body of evidence in the field to suggest not only that intrinsic motivation is stronger than extrinsic motivators (like money), but also that extrinsic motivators can even decrease your internal desire to do something (the overjustification effect).
If the ground is littered with trash around your neighborhood and you like it clean, you will be motivated to pick it up, much like how you clean your house without monetary compensation. Simple as that.
"We should not say that one man's hour is worth another man's hour, but rather that one man during an hour is worth just as much as another man during an hour. Time is everything, man is nothing: he is at the most time's carcass." Karl Marx