Angst? What Angst?: The first book doesn't show any of the Alden kids grieving the loss of their parents or stressed about how they're going to survive. Mostly averted in the movie when Benny asks if they're going to live in the boxcar forever.
Somewhat averted in the beginning when the couple who owned the bakery they spent the night at wanted to send Benny to an orphanage, prompting their moonlight escape.
Archive Panic: This series is infamous for this, currently having well over 150 books in the series including the "special" series of books and the original books by Gertrude Chandler Warner.
Nightmare Fuel: In one book, Jessie is attacked by the criminal and has a bag shoved over her head and tied on. If Henry hadn't heard the noise and run outside... brrr...
Violet's illness in the first book combines this with Adult Fear for Henry especially. You're living on your own in the wilderness on the edge of town, you've just avoided having your youngest sibling sent to an orphanage, and your younger sister requires medical attention that could lead to the family either being taken into care or sent to live with a grandfather they've been led to believe is a monster.
It's never explained how Mr. and Mrs. Alden died, leaving their kids orphaned. There's also no mention of whether the Boxcar kids stuck around long enough for the funeral and there aren't many details on the kind of lives they led prior to their parents' deaths.
These questions are actually answered in the 2012 book The Boxcar Children Beginning: The Aldens of Fair Meadow Farm; the parents died in a car accident, and the children left before the funeral to avoid being split up and because they couldn't stay with the man they'd really like to stay with.
We never learn why James Henry Alden had no contact with his son and the Boxcar kids. Henry explains early that he and their mother didn't get along, but this isn't elaborated on.