Do animals ever get food poisoning from eating raw meat?

Yes, they certainly do - but not from eating raw meat per se. Raw meat doesn't cause food poisoning. Contamination on/in the meat does. They get it from eating pathogenic bacteria which may be contaminating their food - whatever that food might be.

Is it healthy to eat raw meat?

To enlarge on Baker's answer, the human brain is a costly thing, which adds 20–25% to overall energy requirements. Also, as a result of the large brain, jaw muscles are smaller and weaker compared to other animals, even apes. Eating unmodified raw meat, as shown