So, just to start off: I won't be able to go through The Painted Bird to comment on every instance that Kosiński and whether it lines up with history. That would be the work of a journal article or even a monograph and would just exceed the frame of what is possible in this forum.

Originally, Kosiński indeed did claim the book to be autobiographical. This however is not entirely accurate or at leas only on a certain level. Kosiński had spend the war not wandering the Polish country side but rather hidden in the village Dąbrowa Rzeczycka thanks to a Roman Catholic Priest that issued them forged papers and a Polish family that was willing to hide him and his family under great threat to their own life. Despite initial insistance to the contrary, Kosiński's book is a novel that is at best semibiographical since it can be assumed that he was at least able to work some of the things he and his family experienced during the war, especially regarding being hidden, local anti-Semitism and the constant threat of Nazi violence in the novel. Another experience that made it into the novel is that Kosiński did indeed become an altar-boy while he was hidden and his family visited the local Church as part of their cover.

To fully grasp the character of this particular book, I think it was best written by Jerzy Jarniewicz in the article The Terror of Normailty in Jerzy Kosiński's "The Painted Bird" in The Polish Review, Vol. 49, No. 1:

The problem with The Painted Bird is that it cannot be treated as an example of a wholly fictional work which bears no relation to history, nor as a blatant literary mystification on par with the cause celebre of that suspicious genre, Binjamin Wilkomirski's Fragments, nor as a documentary standing alongside Anne Frank's Diary. Stemming from the actual traumatic experience of the Holocaust, relying on what Sue Vice calls the author's historical and ethnic authority (Kosinski was a Polish Jew who survived the Holocaust), The Painted Bird is a hybrid, a bipolar novel, in which history is interlocked with imagination, fact with fiction, autobiography with myth. Interpretations which focus on only one side of these oppositions fail to do justice to Kosinski's literary endeavor.

Kosiński's novel endeavors to incorporate the violence of the German occupation of Poland and the Holocaust into a literary painting of a Hieronymus Bosch-esque hellscape where both the massive violence that occurred and its traumatic impact on the people who experienced it are interwoven in a tapestry of a narrative borrowed from mythology. It takes inspiration both from a sort of Odyssey story as well as from what the Germans call a "Bildungsroman", which is a literary genre about the psychological and moral growth of the protagonist from youth to adulthood. This is among the reasons why the book is so vague on the specifics of the main character, never explicitly stating he is a Jew or "gypsy", why the geographical details are so hazy and why the protagonists journeys through the various villages like an Odyssey or like letting your gaze wander from detail to detail when viewing one of Bosch's paintings. It is also why some of the scenes of violence evoke Holocaust imagery (burning flesh, thin threads of smoke rising) while others (the blinding of ploughboy) are devoid of a racial context but serves as an indictment for the general violence that accompanied the Nazi occupation of Poland and the general devolution of society under occupation into chaos and terror.

This genre, so to speak, is also one that is not limited to Kosiński's work or even just to books. One of its recent manifestations that was hailed for its masterful work was Pan's Labyrinth. While this movie was more on the nose with its mythological parts, it too dealt with the implications of the Spanish Civil War and Francoism by interweaving it with mythology. Another example would the be the 1985 Soviet movie Come and See (Иди и смотри), which also sees a young boy in Belarus observing the cruelties of WWII interspersed with dream like sequences that deep dive into the mythological and imagined but uses these as a way to focus on trauma and the effects of the very real violence.

But as to the heart of your question: Is there historical indication that cruelties such as described in the novel took place? And the answer to that is pretty much yes. Maybe not exactly as described in the novel but there is no shortage of documents proving the inhumane deeds of the Nazi occupation of Poland and Eastern Europe in general. Take e.g. this description from the Kharkov Trial by an Einsatzgruppen translator:

Prosecution: Tell the Court what you know about the shooting of children in the Children’s Hospital of Nizhne Chirskaya.

Bulanov: On August 25 and 26, 1942, I—together with chauffeur Blokhin—was ordered to get the trucks ready. We were ordered to drive them to Nizhne Chirskaya Children’s Hospital. Upon our arrival, Gestapo men [In Soviet Trials, members of the Einsatzgruppen are often described wholesale as Getapo] began to lead the children out of the hospital and load them on the trucks. The children were ragged, and swollen from hunger. Many resisted and would not board the trucks. The Gestapo men assured them they were going to their uncles and aunts in Stalingrad. Some children yielded to persuasion and got on the trucks, while others resisted. The Gestapo men forcibly put them in and I was ordered to fasten the canvas at the back of the truck. Three to four kilometers from Nizhne Chirskaya, a pit had been prepared. Having reached the pit, I and other Gestapo men began to take the children toward the pit near which stood a Gestapo man, Alex. Point-blank he shot the children in the head with an automatic rifle and then pushed them into the pit. Seeing this, the children struggled and tried to break away, crying, “Uncle, I am afraid!” and “Uncle, I want to live, don’t shoot me!” and so on. But the Germans took no notice of this.

Prosecution: What was the age of these children?

Bulanov: They ranged in age from six to twelve years.

Or the historical evidence offered by Klaus Michael Mallmann in his article "Mensch, ich feier heut den tausendsten Genickschuß". Die Sicherheitspolizei und die Shoah in Westgalazien (Man, today I am celebrating my 1000th neck shot. The Security Police and the Shoah in Western Galicia) where he found evidence for the Nazi Security Police in Western Galicia not only killing about 20.000 Jews but also, and he is quite explicit in that, deriving entertainment value from killing. Mallmann cites such as as putting explosive in the Jews' bags and then letting them force them to do a footrace with the police men standing near by laughing as people would blow up; forcing Jewish girls to get naked and using their buttocks for target practice; or when one of them shot their 1000th Jew having a big party for him (hence the title of the article).

As I have described in this older answer, what the Nazis were doing was to turn murder into sport, into entertainment, revel in their victims' suffering, laugh at their gruesome deaths and dream of new and more inventive ways to inflict pain on them.

And in this sense, some of the cruelties and violence Kosiński describes in his novel might be fictional in the sense that they might not have occurred exactly as he describes it but they are historical in that things such as mass rape, thworing children into liquid manure, shooting the patients of a children hospital and inventing ways to turn murder into entertainment were things that are underpinned by historical evidence and did indeed occur.