Young vampire boy murders family dog.

In Cult, a guinea pig gets put into a microwave.

They get sacrificed for witchcraft

Several seasons have bugs

Perhaps the one animal/thing that is safe from American Horror Story

In the newest season, AHS: Apocalypse, a horse dies in the first episode. It was shot in the head.

not sure why there are so many nos on this, there are multiple scenes showing and describing a character killing and mutilating cats

Coven

Heroin use is prominent in Hotel.

There is an addiction demon and heroin use

A man burns his family alive in Murder House. A witch is burned at the stake in Coven.

In season 5, there is an (imaginary) scene where Sally's teeth all break of and fall out, continued with blood.

there is forced amputation pictured in season 4

Drug OD seizure

Coven

Roanoke

In Cult, a man is hung from the ceiling with hooks in his chest, and another man has nails shot into his head. And there's a "haunted house" of sorts where real people are being tortured and killed.

there's various depictions of parents dying in varying levels of gore throughout the series

Yes in the beginning of s1e1.

A couple gets kidnapped in hotel and trapped behind a wall

Seasons 1, 3,4,5 and 6

Seasons 4 and 6 have many clowns. Season 5 has a character briefly in clown makeup

It is mentioned that Kai stalks several people in cult

Oh yes. The devil possesses people in almost all of Asylum and there is a horrifying exorcism scene in the second episode.

Quite a few

The entire show is pretty much gore mixed with jump scares, mixed with a heavy helping of 'whaaaaaaaaaaaat?'

A person's friend shoves their fingers in her mouth after she overdoses on pills, and she throws up.

It's used in Asylum, for one person it is used as gay conversion therapy, and for another it fries her brain so much that she forgets her own name.

There's an entire season.

Many

“They don’t call me hypodermic sally for nothing” -Sally (hotel)

In Coven

In season 1, Violet commits on screen suicide by overdose. It seems that she is saved by Tate but later episodes reveal her body being infected with flies.

Season Seven (cult) has a major part about fears/anxiety and panic attacks

Season 3

A girl with downs is abused but it’s not because she has Down syndrome

In season 1 a character accuses her partner of gaslighting her, but it is because supernatural things are happening to her that her partner doesn’t witness or believe. She is placed in a mental institution as a result, but her partner later believes her and apologizes.

Season 1 in particular has several scenes involving self-harm.

A woman with a phobia of being buried alive is locked in a coffin until she suffocates.

Season One - Episode 1 or 2, there's an entire scene that's based around strobe lighting

in season four, there's a scene with dubious consent involving an exploited birth of a child with a disfigurement.

In season 1 a character dies in childbirth.

The first two seasons heavily play on abortion and season 5 an abortion is shown

In seasons 1 and 6

In Cult, a man tries to get his sister pregnant, which she doesn't want.

almost every single season of AHS has some type of sexual assault in it

There is a trans woman in season 5 who is misgendered and an intersex person in season 4 who is misgendered

In season 1, a gay character is told his relationship is an “abomination.” In season 2, the words “colored” and “negro” are used. In season 4, “freak” is used as a derogatory term for the performers at a freakshow.

in season 2 there is a woman who believes she's anne frank and a n**i doctor. as well as flashbacks from Auschwitz

coven

Deaths of two gay characters in Season 1 Death of a lesbian in Season 2 Death of two gay characters in Season 4 Death of two gay characters in Season 5 Death of a lesbian in Season 7

In coven a person says the n-word

S4E2: two male partners are referred to as "fruits" and it is suggested by a character that they are sick and lower than "freaks".

In season 4 a lot of the freaks are being discriminated and there is ableist language used against them I think

not very many, only a few, and those are in AHS freakshow, where the fat women is that they call ima wiggles.

Santa is a rapist/murderer in Asylum.

most have bittersweet endings

Yes. A lot. In every season.

adelaide is hit by a car and died in season 1

There is a scene where a woman gets buried alive in cult, but it is a dream

In apocalypse that’s what the season is based on

A family is hung in season 4, but only their legs dangling is shown. Season 1, a man is hung by ghosts.

All of Constance Langdon's children, all of the Countess' children, and many more Especially Kyle Spencer, that was absolutely nauseating

There's a mass shooting in Cult "Midwestern Assassin"

A girl's head is held underwater until she drowns in Season 3.

There are car crashes in multiple seasons

In a number of seasons there are the following: Drowning Trapped in tight spaces with no air Choking Throat slitting and the gurgling that follows Use of chloroform