Translation:According to my book, all animals can swim.
No, that is not correct. "Alle" works like an adjective, so you can't put an article behind it. You can say "Al de dieren", however.
But it's much more common to use "alle dieren" for both and rely on context.
al die dieren= all those animals
There's no difference between elk dier and ieder dier, apparently. Just asked my partner, who's a native speaker.
Hope this helps!