S1E1 - At the ambulance, when he steps out to pee, he sees a dog, but the dog is dying. The dog has blood dripping out of its mouth, but it doesn’t die on camera.
When they fight in the ambulence, he gets injured in the neck. It's bloody and he doesn't make it. Around 43min. It will also be in the recap for episode 2.
He falls underwater briefly, and the water's murky so it may be a bit scary (and unsanitary), but nothing bad happens. It's also not a natural body of water / it's flooded subway area.
S1E1 - A dog is seen near an ambulance with blood dripping from its mouth, but does not die on camera. Mice/Rats are seen running through the streets, and when the mass leaves, there are bloody mice/rat corpses left on the ground. Deer and mouse are the first dead animals shown, but are already dead.
S1E1 - There are a few animal corpses shown. The first is a bloody deer next to the side of the road, the second is a bloody mouse in the corner of a room.
S1E1 - The mother walks in to find her son dead in her bed with her also dead husband. Later in that same episode, a woman is seen wailing for help and carrying her dead son through the chaotic streets.