There's dog-like monsters that can be killed. Sometimes the dog-signifier is in the species ("Kath hound") other times it's in the descriptor ("guard dog," "Separatist hound")
MOST times, companions will only die as the result of your intentional, informed decision for that to happen. Exceptions with mild spoilers to follow: Major NPCs die in the Trooper and Jedi Knight stories. One of your companions dies in the Knights of the Eternal Throne expansion. You have to pick one out of two and can't save them both.
The Sith Warrior is ordered to kill a man and bring his severed hand as proof. You can choose to spare him, and he will cut off his own hand for fake "proof." (semi-offscreen, close up of his face)
The Sith Inquisitor grew up as a slave, Kira Carsen (Jedi Knight companion) was abused as a child, and Thexan, Arcann and Vaylin were abused as children, with Vaylin's abuse being explored in some detail
There are people called Spice Traders, who sell drugs called Spice. There are also other various times where people can mention selling spice or using it.
During the casino nightlife event, there's a mechanic where you can drink alcohol to get a "feeling lucky" bonus on the slot machines. If you drink too much to chase this bonus, your character will die.
I don't think it's possible to play without having to kill animals at some point. My best tip for minimizing this is to play a class with stealth ability. That way you can sneak past most of them, and then at higher levels, you can use it to end combat if you accidentally "aggro" any.
Stealth classes:
1. Jedi Consular -> Shadow
2. Smuggler -> Scoundrel
3. Sith Inquisitor -> Assassin
4. Agent -> Operative
Not only is there unavoidable animal abuse but the game itself is pro-animal abuse. Animal rights activists are exclusively portrayed as ignorant and in the wrong, even when they're fighting abuse as terrible as baby animals being forced to dogfight and the last members of a species getting eaten.
Many boss battles where you fight someone and their pet monster. And then there's dialogue where the boss mourns the pet when it dies. Some of these are optional such as the Eternal Championship arena and the Ravagers operation.
A character boasts about using his job as a doctor to creep on women. You can optional flirt with a woman you have enslaved, but you can't romance her. You can also optionally sleep with prostitutes and trick a prostitute into sleeping with you for her freedom. Then not free her.
There's a smuggler ability called "dirty kick" with a visceral sound effect. Even if you don't play a smuggler, you'll still encounter it whenever you fight smuggler players or NPCs.
Every storyline has points at which you can torture other characters, or the player character will be tortured. It's a very common occurrence in this game, sometimes but not always optional, and would be a difficult trigger to avoid in my opinion.
No excessive gore but a bloodless decapitated head is shown prominently and put on a spear as part of a quest (haven't played yet so I can't say how gory it is for sure) and there's another mission where you put a skull in a large pool of blood.
The Knights of the Fallen Empire (and Eternal Throne) expansions feature this more prominently, viscerally, and PERSONALLY than just about any other media ever written.
There's an instance of the trope where a character is only known by a nickname, and then it's played for laughs when their "stuffy-sounding" birth name is revealed.
(One of the Jedi Knight companions)
One of the Imperial Agent companions is a "mad scientist doctor." The planet Taris has broken down hospitals. In some of the more recent content, a major NPC is hurt and there's a recovery scene in a hospital type environment.
In MOST cases, the "madness" comes from some kind of dark side corruption rather than a real world mental illness. (The Dread Masters storyline is a good example of this.)
The game considers the dialogue option for a male where he says he wants to wear a feminine dance outfit a joke and it’s treated as such. The lines might be the same if your character is a woman but I’m not sure.
Not nuclear, but there's a lot of explosions and detonations. If there's such a thing, it probably wouldn't be called nuclear but something more space-related I guess?