About the controls, yeah, they lack precision, the horizontal speed is way to much compared to vertical, i believe some acceleration would help on it yeah, would be great to also reduce maximum speed to avoid running faster than flash ^^
not talking about locking the level but making it a bit bigger, and better separate the different areas, you don't have to lock the player and prevent him from coming back, you just have to present a problem, then lead to a solution, here's some rough drawing for what i said about the whale, keeping in mind that the first level introduces the bird and the multijump, here's how you could design the first part of the second level :
The player know he needs the bird to get up to the top right corner, he would see the water tunnel connecting the two areas, but when entering the water he would notice he can't swim up, the only way he can go is down, where he will find the whale which will obviously be the swimming up ability, this way the player know what it allows him to overcome, it doesn't have to be this straigth forward all the time, but it is better to present a obstacle, then either it leads to something that allow you to overcome it, or later on when you find something new but not particularly linked to anything it will make the player wonder about what it does, then he might think about that passage with water he couldn't get to some passage, he would then want to come back and try to use a whale here.
Also, about the checkpoints, you shouldn't make the game save each tim you pick an animal (if it's the first time maybe though) because if you get stuck to some place and pick an animal it would save to this point but you would still be stuck when you reload.
Lastly, the end of the second level i ended up having all animals in the same place, picking the right one was really hard, maybe holding Z could bring up a menu to select one of the animals which are in range of being grabbed ?
Hope it helps and that i'm not to harsh.