I can only recommend reading his works, they are deeply profound.
That really depends on the culture you are coming from.
There is a deep divide between how European and USA culture views what is appropriate material for children.
Being from the nordics, H.C.A's whole collection was part of mine and every friends childhood, from as early as kindergarten, and I vividly remember feeling deep sadness and empathy towards some of his characters at an early age.
I did enjoy them as kid - as sad as they were. Many years after I can't think of a reason to consider them: "most certainly not appropriate". That's being overprotective.
In the light of the current events - they should introduce an age check verification to readers, right?
FWIW, when (spoiler alerts) the little girl gets her feet cut off in red shoes my 8 and 10 year olds were shocked at the turn events, but hardly shaken. Likewise when the little match girl died in the cold they were sad, but not permanently so.
It's the same deal with grimm fairy tales, or even pinocchio (pinocchio gets hanged).
It must have been an abridged version or something that skipped the redemption arc, like this:
"In the end, the Prince marries another, a girl he thinks is the girl that saved him, but of course, isn’t. And the little mermaid is given the opportunity to win back her life with her family, to return to life as a mermaid, if she can kill the Prince as he sleeps. But, she loves him, and so she can’t.
Instead as part of the bargain she made with the sea witch, she dies, turning into sea foam."
That left off the redemption arc:
But here, Andersen is able to deliver the ultimate judgment. Instead of simply perishing as sea foam as other mermaids do (we are told earlier that, unlike humans, mermaids do not have afterlives), the little mermaid becomes a daughter of the air. In exchange for her goodness, for her suffering, and her loyalty, she is given the chance to win immortality, to win an immortal soul.
https://thecuriousworthy.com/2017/03/30/the-original-little-...
Indeed, Max and Moritz ending up in the meat grinder (literally). Also reminds me of 'little riding red hood' originally lacks a happy ending at any rate.
(As for age, I think I was 6-7 when I first read Han C. Andersen)
This is not always the easiest thing to guess. The things that gave me nightmares were people looking at me through mirrors (i.e., Snow White), animal brutality (which featured prominently in 90s family movies), and adoption (i.e. getting adopted into the "wrong", abusive family). Meanwhile I ingested astonishingly violent material and slept like a baby. I think it's hard to figure out what kids will identify as fantasy and what they'll see as a real, yet-unknown risk.