What impact do the groups the boy comes in contact with have on his individual freedom?In particular, on the basis of mob mentality that causes all of these terrible acts.
Kosinski's The Painted Bird is, not exclusively but still importantly, a presentation of Polish villagers' attempts to take away the narrator's personal freedom, and the narrator's attempts to get it back.
Much of this is obvious. People repeatedly attempt to kill him, for instance, which certainly is an attempt to take away his personal freedom. He, in turn, finds ways to stay alive (by pulling his would-be executioner down the hole and into the rats, for instance). And when they're not trying to kill him, they constantly beat and abuse him, sometimes stopping the abuse only when it's time for the boy to work.
This cause and effect is illustrated by the narrator's use of what he refers to as a comet, and applies specifically to his defense against mobs. The boy learns quickly (again, an example of his adaptability and his attempt to hold on to his personal freedom) that he can defend himself against mobs with a comet. Mobs seek to beat and abuse him (take away his freedom) and he seeks to defend himself with a comet (hold on to his personal freedom).
Thinking of personal freedom, in this case, might be easier if you think in terms of power. When villagers take his power, they are taking his personal freedom. When he adapts in order to achieve power, he is seeking personal freedom.
Again, examples of attempts to take away the narrator's power abound in the novel and are obvious. Perhaps the most significant examples of his attempts to regain power (achieve personal freedom), however, are the spiritual attempts he makes: first obsessively repeating prayers in order to earn indulgences, then later attempting to become evil, as those around him with power are evil. In both cases, he is seeking the help of the unseen. Of course, neither attempt is successful, and the boy, as always, survives though his own wit. But his spiritual attempts are examples of his struggle to be in control of his own life and destiny.
In short, the novel forms a pattern of villagers taking away the narrator's power and freedom, and the narrator trying to take it back.