Parents in the books are almost universally described as good: the sole exception is Denethor, who is rather cold in his treatment of his adult son Faramir, but it is not framed in an abusive fashion so much as a willingness to use Faramir as a gamepiece in the war.
A character claims there to be a rumor that the main character's parents killed each other, but this is almost certainly made up. Another character spreads a rumor that the main character murdered an eldery caretaker but we know for a fact this is false.
Early in their journey, the Fellowship is attacked by a large pack of wolves and kills many of them. Gollum eats a number of fish over the course of the story, and kills some rabbits. A number of creatures resembling giant elephants are killed in battle by the protagonists.
King Theoden's horse, Snowmane, dies at Pelennor, with his death being framed as a tragedy due to the fact that he also crushes his rider while falling. About a paragraph is dedicated to him being laid to rest.
A main character has a stalker and it is heavily implied that they intends to sa them. Some other characters are stripped or groped in a creepy and intimate way that may bring up imagery of sa and are threatened with being "played" with and called by terms of endearment (though this is likely threats of other kinds of torture). One of the characters finds it too disturbing to recount later.
A number of characters are held captive over the story: most notably, two characters spending an extended period of Chapter 3 of Two Towers with their hands bound.
No beheadings described but in Book 5 Chapter 4 "The Siege of Gondor" heads of fallen soldiers are catapulted into a city under siege and it's pretty gruesome
There are vague mentions of crushed body parts and a main character is crushed nearly to death in Book 5 Chapter 10 (RoTK). Another main character does die from being crushed in Book 5 Chapter 6.
There is one example in Fellowship of the Ring where the character later comes back to life, as the other commenter mentioned. But there is another example in Return of the King where the character really does die.
The main character's parents are noted to have died some years prior to the books. Two supporting characters lose their uncle, whom they consider a surrogate father, and his own son dies offscreen. Another character loses his father and elder brother. A minor character noted to be a distant relative of the main character dies of natural causes. All deaths are framed tragically.
A major theme is the corrupting influence of power and evil, particularly in relation to Sauron and/or the One Ring. Everyone who has the Ring for a long time eventually becomes possessed by it, though some are better at resisting this than others.
The books take place before the existence of modern law enforcement. The closest thing is an organization called the Shiriffs, who are co-opted into the foot soldiers of a street gang in "The Scouring of the Shire"; they are framed as ineffectual buffoons.
A character dies by suicide, another character is suicidal and tries to get themself killed (but not at their own hand), and another character briefly contemplates suicide but decides against it.
Not in those words but a character explains multiple times that they are going to kill themself in Return of the King and another thinks about killing themself in the Two Towers.
It can be somewhat questioned whether Gollum represents a person with DID, but he is depicted as a character with two personalities, one of which is cowardly and simpering, the other treacherous and murderous.
The hobbits, who are described as well-fed, often make jokes about either their own weight or each other's, which is usually framed in a playful manner. A few minor characters, though treated positively, are largely defined by being fat, including a hobbit named Fatty Bolger and a commander named Forlong the Fat.
On the contrary. Many many characters can be interepeted as aro and/or ace. Obviously, not explicitly called or described like that, but from the context (like the utter lack of romantic partners or interest in such).
There are a few relationships that feature some kind of age gap - for instance, a 26-year-old woman bearing a crush on an 87-year-old man who marries a 2000-year-old woman - but it is not treated as such, as the characters have hugely varying lifespans and nearly all of those romantically involved appear similar in age.
There are a number of scenes featuring male nudity, with the most notable appearing in "Fog on the Barrow-Downs", "The White Rider", and "The Tower of Cirith Ungol." In no instance is it framed as sexual.