No dog death shown on screen. However there is an implication that a dog may have died at the end. The actual fate of the dog is not confirmed one way or the other (in this commenter's opinion the dog would have escaped as that would be more realistic for the narrative)
advance was made and when she pushed him away he says “you know you want this” and tries to push it a bit further but nothing more than that. there were a couple places where assault could have fit in but the threat is barely there at all
At the end of e5 (Demon 79), there is a scene of nuclear war breaking out and fire erupting in a building. Nothing gory is shown in that scene, but it is definitely upsetting and many people are implied to burn. There is also a scene earlier of a room on fire, but nobody is injured (it is vision/hallucination).
E5 (Demon 79) is about a woman who is visited by a demon and told to make human sacrifices. She is not possessed, but there are some moments where she is shown visions, which look a lot like possession. In e3 (Beyond the Sea), a man inhabits another person's (robotic) body, but there's no religious element to it.
Almost every episode includes a scene that could be interpreted as a mentally ill person acting violently, but the mental illness aspect is never fleshed out explicitly. Special warning for e3, both the cult leader character and one of the leads.
Episodes 3 (Beyond the Sea) and 4 (Mazey Day) have explicitly depressing endings, and e2 (Loch Henry) and e5 (Demon 79) are more bittersweet but still sad.