So, is it her son or not and if not, is he dead?
The real-life case on which the film is (probably quite loosely) based suggests:
he’s dead or to be more specific, he was dead at the time. I mean, heck, even if he was alive in 1928, he’d be 90 today, so he’d likely be dead in any case, but you get the idea
the film is based rather tightly on the case. the man who wrote the screenplay uses dialog directly from court transcripts and police records.
no and yes.
I didn’t find the wiki page to be terribly helpful.
So why did the kid claim to be hers? Who was the kids actually? What happened to her and the kid in the end? Was there anything found out about her son, or was it just assumed that he was killed by the chicken coop murderer because it’s a convenient coincidence?
In real life, the kid was a runaway from Illinois who wanted to get to California so he could get into the movie industry (cite). I don’t know what happens in the movie, but I imagine pressure from the LAPD was also part of it.
I’m not sure where the fake boy (Billy Fields) went in the end. Christine continued to believe her son was alive and kept searching for him all her life.
The actual killer, Gordon Stewart Northcott, confessed to killing Walter Collins but later recanted. He was hanged for three other murders, so unless we turn up any new evidence we’ll probably never know what happened to the boy.