it's widely believed and a largely accepted headcanon that Paul is trans and is Care, so my answer for this is a little on the edge. if this is true, then yes, there is birthnaming (and deadname mentions?)
it is very much implied, and i feel as if it is important to note that it at least constitutes a warning. petscop does fact try to lure the viewer into dark places and it wasn't hard to imagine that there was pedophilia on my first watch
Abuse is one of the main themes of the series and while things relating to sexual assault are not (as far as I know) implied by the series, one could perhaps interpret that reading.
there are no explicit ghosts in petscop, but they are mentioned, and a viewer may or may not believe that there are supernatural elements to its story.
One of the children in the game is verbally abused to the point of body dysmorphia and self-loathing. Their father shows them their reflection in a vase and berates them for their appearance.
There's a mention and later scene of a character being stuck in a dark closet. In addition, A character mentions being "trapped" while it is implied they are in a car.
Yes, due to the nature of the YouTube channel's description as well as episode descriptions. In addition, the episodes are uploaded as if for an audience.
no, but there are mentions of characters being born, the word rebirth is used frequently as a way to express the idea of a character becoming "part of the family"
following the "paul is trans" headcanon, this would be true. also important to mention paul is just generally very trans-coded so this may upset people.