To balance out the long lifespans, you would essentially need your animals to have long hibernation periods. You could build a world where as the animal grows, the need for food decreases or that the need to feed regularly disappears. Now since the environment is already saturated with magic, I expect the animals to absorb some of it. If they absorb enough, the magic can help regenerate dead cells at a much faster rate. If this continues for long enough, perhaps the animal becomes essentially invincible (e.g., the moment a sword piercing this snake is removed, it heals from the wound). For particularly old animals (30,000 years) you could replace their biological need to eat with absorption of magic in the environment.
Another thing that you can do is stop the physical growth. In normal world, animals grow up to a certain size till a certain age and stop growing so much once they reach adulthood. 227
It could be the same there. You could remove the reproductive system after a certain age, even replace hearts with pure magical cores.
The skill an animal is learning would also probably depend on their upbringing and inherent abilities. For example, a lame lion would learn speed or stealth while a lion who has generally starved throughout childhood would learn to be a better tracker. For smaller animals you could try increasing their size just enough that its natural predators would be afraid of it.
Lastly, you could make the animals less violent than their normal counterparts. They will generally not pick fights with smaller animals if there is no need. I believe an animal smart enough to learn magic will be smart enough to maintain truce with other animals like itself, i.e., with magical abilities because it will simply not take the meaningless risk just for thrill or food, if it doesn't need it. If you do, however want to make your animals violent, I suggest a specific reason. For instance, if animal A defeats animal B in combat and kills it, A will gain the magical abilities originally belonging to B. 376