I'm pretty sure it is not possible to level them up. Try checking the experience points with the spider, kill something, return to human form, use the spider statuette again and check your experience. If the spider form keeps the experience points, it could be theoretically possible to level up; if it doesn't, then more than likely none of the animal forms can level up.
For the frog, if you are running, archers should not have much of a chance to hit you, unless you are running strait towards or away from them. That was something that annoyed me when I started an archer character; she could not lead monsters at all (ie shoot in front of them to try to compensate for their movement).