Question: How did chief survive getting hit by a train, and falling down, and only ending up with an injured leg?
Question: If the bear died in the fall, assuming the fall did kill it, then how did Tod survive?
Answer: Since we don't really know how he died, he could have drowned and not died on impact. Bear may not have been a strong swimmer or sustained too much injury from the gunshot to swim to the surface. However, in physics, force = mass * acceleration and thus larger creatures will hit the water with greater force than small creatures (as the old cliche goes; the bigger they are, the harder they fall). So it's possible for Bear to die on impact and not Tod because of his larger size.
Question: Tod is only a cub the first time he encounters Amos Slade. Amos swears to shoot Tod the next time he sees the latter on his property. Amos leaves for a long hunting trip the next day and doesn't see Tod again until after he returns home. Tod is full grown before Amos returns. When Amos sees a full-grown Tod in his yard during the night, he yells, "It's that fox again." How does he know it's Tod?
Answer: He fell into the water so he could have very easily broken his leg on something in the water like a rock.