A German Shepard is killed graphically an hour into the film. You hear whimpers/cries and see the body. Look away when the dogs run away from the police officer. Skip roughly three minutes worth from that moment to avoid the scenes.
as a crowd is running out of the museum a few people fall in the chaos, some of them fall down the (admittedly not very steep) stairs to the museum entrance
I'd tentatively say yes - there's a person that gets smashed through the skylight and skewered on one of the exhibits. He's probably dead when be falls but it's not known for sure
Though characters frequently run into restrooms and come across maimed/rotting bodies, there's no vomiting whatsoever.
A small warning: during the film's climax, a woman is smothered against a revolving door and blood comes out of her mouth (implying internal injury) but it is brief.