So were animals immortal, like man, before the Fall?

Perhaps, but this seems doubtful. For one thing, they did not eat of the Tree of Life, which seems to be the best explanation of why Adam was said to be offered to live forever. Death would come from Adam only after eating of the Tree of the Knowledge of Good and Evil, promised at Gen 2:17: “in the day that thou eatest thereof thou shalt surely die.” But it does not say that animals did not die previous to this, and at no point does any Bible verse explicitly link Adam’s sin with the introduction of animal death. Some point to Rom. 5:12 as indicating that Adam’s sin introduced death to the animal world: “Wherefore, as by one man sin entered into the world, and death by sin”. But the same sentence concludes: “and so death passed upon all men, for that all have sinned.” It says nothing specifically about animals, and “death by sin” is too vague to hang a whole doctrine upon: obviously, it could mean only “death of man by sin,” since that is the context. The same problem afflicts 1 Cor. 15:22-23: the remark “in Adam all die” leaves “all” with a vague domain of application: I would be inclined to think it means “all men,” not “all living beings.” After all, later in that same chapter’s argument, the redemption for that original sin is said to make resurrection possible, and that certainly does not include the resurrection of animals.