Do all animals have immune systems?

Yes. Most animals have one which works in a similar way to ours.

In fact, you could say most animals have a better immune system to deal with all the stuff they go through everyday. If humans were to eat the things animals eat every day we'd be dead pretty soon.

Sharks appear to be immune to, or at least resistant to, most diseases we know of.

Animals Immune System

From bacteria to most advanced have immune system. It provide resistance to foreign particles. It may not be so well developed but help to resist few non favourable changes.

Yes :)