Why didn't Ellen use Peter as a vessel to begin with, instead of making do with a girl? Annie said that she and her mother were semi-estranged, going through long periods of not talking, one of which was when Peter was born, but that they were speaking when Charlie was born, and Ellen doted on her. Maybe whatever preparation needs to be done to a vessel is best started when the vessel is a baby.
The miniature Annie turns around hints at the answer and the conversation she has with Charlie about Ellen's attitude to Annie's mothering. Annie says when she was pregnant with Peter her mother "made" her have him. She says during the group therapy that Ellen was in and out of her life in terms of estrangment, so when she was pregnant with Peter her mother was "in" her life but when he was born Annie kept him away from Ellen which was really messing up Ellen's plans. No matter, Annie gets pregnant again, but shit, it's not a boy, which is necessary for the ritual to work. Annie tells Charlie that Ellen fed Charlie as a baby, which we assume at first means like with a bottle or baby food. NOPE. The miniature depicts Annie in bed breastfeeding Charlie, and standing next to her is a doll of Ellen with her breast exposed, ready to take over feeding her grandchild. Who else would Ellen have breastfed? Her daughter Annie (unsuitable for the ritual but does get possessed later) and her son who hanged himself supposedly because he was schizophrenic but probably driven to suicide by his crazy mom trying to turn him into a demon's vessel, before the ritual was completed. Ellen must've thought she needed to get to a baby ASAP to prepare them for the ritual and could work around the child's gender. She nurtured Charlie in more ways than one, hence why Charlie is the only one who misses her, but as the text in the information about Paimon specifies, giving him a female host makes him "livid". Peter never liked Ellen, mistrusted his mother (even if she was unconsciously trying to save him from a worse fate by killing him earlier), he was never going to be easy to possess unless he was "replaced" with Charlie.
When Annie sees Joan in the craft store the audience is left to wonder what Joan is actually buying there. If they paid attention to Joans trunk they wouldve seen that she had just purchased a chalk board. The same one she uses at her seance. A subtle clue that shes lying about having a son.
Why did it take so long for the cult to implement their plan to kill Charlie and transfer Paimon into Peter when a female vessel was supposed to have displeased him, especially as Ellen would've had more time to benefit from Paimon's theoretical satisfaction with the new situation when she was, y'know, alive? Ellen must have arranged for Charlie to die specifically after her own death; she had already inadvertently killed two members of her family (her son, her husband) and evil as she was, she did love Annie and might have felt enough conflict and regret to put off the murders of her granddaughter and grandson so she wouldn't have to experience that as well - or as she at least cared for Annie, she didn't want to have to see her daughter go through that or possibly die as a result of the plan.
When Charlie is following the glowing light outside where she sees (possibly) a vision of her grandmother sitting before a fire, foot prints can be seen on the ground next to her, indicating that someone had ventured out to the same path recently. Considering that the Graham household is somewhat isolated, it was either one of the family members (which doesn't seem too likely as there is nothing of interest on that path) or it belongs to one of the cultists who'd been skulking around the property.
After Ellen's funeral as the Graham family is returning home, we see the inside of the house before they enter. During that brief moment, footsteps can be heard inside the house, letting us know that someone (or perhaps even several people) not only have access to the house but are sneaking around inside of it. This would explain why the door to Ellen's bedroom is inexplicably open as well as several strange markings and scrawlings being found around the house.
During Annie's nightmare when she tells Peter she never wanted to be his mother and attempted to have a miscarriage, Peter accuses Annie of trying to kill him. Annie cries that she was trying to save him. Before this, she had a sleepwalking episode in which she doused Peter, Charlie, and herself in paint thinner, planning to immolate all three of them. Word of God confirms that Annie knows on a subconscious level what her mother and her cult is attempting to do to her and her children and that she's attempting to spare them a Fate Worse than Death by killing them before they can be used as demon vessels.
Upon my fourth or so viewing I realized something. Word of God says Paimon was Charlie from his/her birth. I started to wonder. Charlotte is the feminine form of Charles and can also be shortened to Charlie. Do they all call her Charlie in a subconscious effort to placate Paimon's wrath from being locked into a female body?
We know Charlie's body was in the car, but we don't know she was fully decapitated until that horrific shot of her head in daylight. We don't see that car again or hear about what happened to it. Later we see Annie has made a 100% accurate miniature of the scene, including the telephone pole and the approximate location of her daughter's head and what it looked like, describing it as a "neutral" view of the accident. She has a nightmare specifically about ants crawling over herself and her son's face. And at the end Charlie's head has been stolen by the cult and placed on the mannequin. So how does Annie know what the accident looked like and how did the Graham family get the head back to bury with their daughter's body? The answer must be: when Annie has her breakdown upon finding Charlie's body, Steven must've been the only one able to ask Peter what happened, and called the police. The body would be taken from the car in a bag, the car impounded, the back seat "black with blood" as Annie describes it, and probably destroyed later because who the hell would want to drive it again. The police must've driven Peter, Steven, and Annie (who might've insisted despite clearly needing sedatives to stop screaming) to the site of the accident to file a complete report and retrieve Charlie's head. It was dark, Peter was high, he went into shock, his mother is hysterical, his father is trying to keep it together, and he has to say "no...no...no..." to every telephone pole they pass by until they spot the head. Now the whole family is triply-traumatized (first by finding the body, second by the fact that Peter is responsible and didn't tell them until it was too late) by seeing what Charlie's head looked like, smashed-in and partially consumed by nature within a couple of hours. That's an image none of them can scrub from their minds.
Annie's attempt to burn Peter and Charlie alive to spare them gets a whole new horrific level with the revelation of what possibly happened to Joanie's son and grandson, suggesting a prior attempt at possession and sacrifice that didn't pan out (and maybe could've spared them).
At the end of the movie, Peter sees Annie's decapitated body supernaturally floating up into the family's tree-house where the demonic church resides. When he goes to investigate himself, he sees both his mother's and grandmother's corpses bowing towards the Satanic statue with Charlie's decapitated head on top. After Joan crowns Peter, he turns to see that his mother and grandmother's bodies have turned to face him, continuing to bow with no indication that anyone moved them. It's possible that Annie and Ellen are doomed to be servants of Paimon, even in death.
After Peter is possessed by Paimon in the finale and climbs up into the tree-house to find cultists and his mother's and grandmother's corpses prostrating themselves before him, he also looks at a picture of his grandmother placed on the wall of the tree-house labeled "Queen Leigh". Paimon is referred to as "King" Paimon, so if Ellen is the "Queen", this has some pretty disturbing implications. Peter's soul may have been removed from his body but it is still his body.
This family takes an extraordinarily casual attitude toward Charlie's health.
Charlie has a lethal nut allergy, yet on two separate occasions her parents let her go out without her Epipen.
Peter clearly adores Charlie, but he doesn't think of the Epipen when he takes her to the party.
Nor does Charlie herself think of it, despite being fourteen and plenty old enough to think of such things.
Nor does Charlie think to avoid unknown food, or even to ask someone whether the cake has nuts in it.
I honestly considered her not checking or 'forgetting' about her allergy could have been the influence of Paimon, since she needed to die. It would make sense that the demon would influence her to put herself in danger. The family doesn't have any excuse though.
A line of stage direction from the screenplay reads: "Charlie turns, digging into the cake. (Nuts are visibly a key ingredient.)" This implies Charlie knew exactly what she was doing. However, a later line of stage direction reads: "She stops for a moment to SWALLOW. She pauses, then swallows again. She looks slightly concerned." This implies she was simply careless.
This could stray into theory territory here, but I feel like this applies to her mental health as well. We know she has demonic influence but in general the family seems very okay with her odd behavior. She's 13 years old, but looks and acts much younger, to the point of playing with toys in class. Her hair always seems messy and while she can speak normally, she tends to give short and rather emotionless responses. I feel like most families would...I don't know, maybe get her checked out? Of course the movie is vague and the family might have done this, as Annie forced her to go to the party to "talk to other kids".