There are multiple occasions where you have to fight dogs and kill them, but they do not appear in cutscenes. The dogs you have to kill look very much like your dog companion from "Dragon Age: Origins", so it can be distressing.
Mages frequently become so jaded, hopeless, and burned out on injustices that they resort to violence especially at the end. (MAJOR SPOILERS) Orsino turns to blood magic and attacks you, forcing you to kill him. Anders blows up the chantry and you can at least protect him from the templars and various other characters. (No amount of siding with the mages or romancing Anders can prevent any of this.)
There are some characters who can die unexpectedly and some characters who will die no matter what you do. (SPOILERS) If Hawke's sibling goes to the deep roads, they will die unless the other party member is Anders. Near the end of the game, Hawke's mother dies. At the very end of the game, both the head mage and head templar die.
Very very unreliable narrator. Lots of use of the trope where something happens in the story and then it gets questioned, and then we cut back to the story something different happens instead.
Some of the dialogue from Hawke's mother has themes of emotional abuse especially relevant for eldest children. Relying too much on them, blaming them for things, etc.
If you rival romance Anders, who is both possessed by a spirit and mentally ill, you basically gaslight him into thinking he's wrong about things he's literally seen happen in the mage prisons.
Many mentions, but rarely anything on screen. Fenris for one, many many mage children mentioned for another. The Templar character Ser Alrik is seen threatening a young girl to (essentially) lobotomize and abuse her as he has been doing to others throughout the game.
There are several references to templars being addicted to lyrium, including a minor character who is going through withdrawal. There are also some minor characters who may be implied to be alcoholic.
The player character has a war hound that can accompany the party in combat. During Act 1, the protagonist's uncle is also verbally abusive towards the dog and it is somewhat implied that he is neglectful towards it when the protagonist is not home.
You can choose not to kill dragons, but there are many instances of baby dragons and two fully grown dragons that must be killed for you to do major side quests.
A character potentially commits suicide by fire magic in the quest "Shepherding Wolves". Mages, both allied and enemy, may use fire spells in combat, though it's possible to limit this by not choosing or disabling fire spells for your party. Other enemies include fire-breathing dragons and fiery rage demons, who may knock out your party members. There are also a few instances where you may come across burned corpses, and a major antagonist is killed in a way reminiscent of burning alive, but no actual fire is involved. Finally, the major religion in the games is centered around a martyr who was burned on a pyre, and some text and dialogue references this.
In addition to references to children dying, one of the player character's younger siblings, who is about 18-19 years old, dies early in the story. The other can die depending on player choices.
A character's mother is killed and reanimated for use in a ritual. Not extremely gory but the scene is rather upsetting due to the nature of her death/body.
Several characters close to the player can be kidnapped across various quests, potentially including their mother, their brother/sister or their love interest
You can attempt to romance more than one person, but generally once you have progressed far enough with one relationship, you are unable to romance anyone else.
The DLC questline 'Legacy' heavily features the ghost of your father, though it is easy to see it as ghosts of memories or a sort of magic-based diary that shows a ghostly projection of him. Additionally, the 'Haunted' companion questline for Varric in act 3 references ghosts, and has some ghost-like moments.
I should add to the above comment that the possession is largely consensual - the character agreed to become possessed - but the spirit at times causes the character to lose control of his emotions, and it is implied that the spirit is influencing him and his actions.
Your companion Aveline is part of the city guard and her actions are largely unquestioned. Additionally the narrative's tendency to sympathize with Templars over the mages they are the literal jailers for could be seen as copaganda.
One of your companions works as a healer for the poor, and when you first meet him, he is using magic to heal a child that is injured. There is no gore or trauma shown, and it is a brief scene.
Anders (who has bipolar disorder) has a few anxiety attacks in the main game and in Legacy DLC. Merrill also has a few scenes where she is very anxious.
The characters travel through narrow caves and corridors, but are never in danger of being trapped. The main setting (Kirkwall) is kind of a claustrophobic place, with high walls, narrow streets, and many underground passages and areas without much natural light.
There is a quest that can end with a character intentionally burning himself to death after a long discussion about it with the player character. The only way to avoid this is to hand him over to be executed.
Some of the dialogue about Sandal, who is autistic-coded, is kind of ableist. Characters can also be very hurtful towards Anders (who has bipolar disorder and is severely depressed by the end of the game) and Merrill (who may be mentally ill, though it's not specified) in a way that borders on ableism.
Basically. In the Mark of the Assassin DLC, you can encounter an NPC who has a female elf model but a deep, masculine voice, and Tallis says to "back away slowly". It's not very nice.
The player character's family's appearance matches your choices in character creation. If you make Hawke Black, their family members will also be Black, and their brother or sister is the first character to die.
Particularly aimed at mages and elves though dwarves also get a little bit. Elves face racial slurs, ghettoization, being treated like petty thieves, having been made slaves and not being allowed in settlements. There is at least one in universe slur aimed at elves. Many quests deal with the plight of elves in the city and hightlight their treatment. One character is a former slave and his experience is not always respected by other party members.
Mages are distrusted, often face sever physical and emotional abuse, are imprisoned and threatened with magical lobotomy. Most characters shy away from or openly display distrust of mages. One party member will constantly spout his distrust of mages at your other mage party member.
There is no explicit sexual content, but there is plenty of innuendo and some fade-to-black sex scenes. There's also at least one scene (in The Exiled Prince DLC) where the party interrupts a sexual encounter between NPCs, but the characters are in underwear.
You can encounter many homeless people throughout the game, especially in the area labeled “Darktown” which you have to go to often to progress the main story.
You end the game with your entire family dead including your father, mother and one (possibly two) siblings, a war just started over the horrific oppression you've witnessed all game, and the PC fleeing their home -again- and on the run / known as a dangerous criminal or potential war hero.
The game could alternatively be titled How Hawke's life just kept getting worse: The Game". ABSOLUTELY not a happy ending.