First of all, I love this game. I doubt I'll stop playing it anytime soon. But I do have a few suggestions to make this game even better:
1. An animal storage den - similar to Dragon Story. Obviously I'd prefer unlimited storage, but even being able to store 5 animals would help greatly.
2. Please lower the cost of expanding. I rarely have enough coins to feed my animals, compete in tournaments and expand. Which brings me to...
3. Make it easier to obtain coins. I've been playing FFS only a month or two less than DS, but I'm so much farther along in DS because coins, food, habitats, and expansions are so much easier to obtain.
4. In the main battle arena (non-tournament), please allow us to see beforehand who we are battling. It would help tremendously in picking our fighters.
5. Also in the main battle arena - please add the type-name of the opposing animal (Frostfang, Pandaffodil, etc.)

I may add more to this list as the thought occurs to me