If an animal on Earth develops human qualities, such as noble sentiments and intelligence, will it remain an animal without a chance of further evolution, or may it in time step over into the human realm?

Evolution is part of a natural law. It has a mainstream and many tributaries, but all are part of the same law. The spirit within you is the same spirit that is within the animal. There is no difference in essence, only in degree, so there is always a chance for further evolution.