"Des" changes to "de" when followed by an adjective that comes before the noun. Further examples: "de grosses souris" ("fat/big mice"), "de jolies filles" ("pretty girls").
No, the "s" in "Plus" is silent here. A simple rule to remember: the consonant at the end of a French word is silent unless it is a "careful" consonant. In other words, if the word ends in C, R, F or L, you pronounce the last consonant, otherwise not.
Not completely correct. If you heard someone pronouce "Plus de petits animaux" with no "s" (an no other words), what you'd probably be hearing is "plu'd'petits animaux", which means "no more small animals". Rule of thumb: the "s" is never pronounced for negative "plus" (i.e. ne ... plus), meaning "no more" (as in "they're all gone"), and it's generally pronounced for positive, meaning "more" like here, to mark this difference (this is an informal thing which is "technically" wrong but everyone does, in my experience). For a more complete explanation:
How can the translation mean two different things? One says there is "More small animals" while the other is "No more small animals".
See my above reply - the distinction is usually made via pronunciation, something Duolingo seems to be neglecting in this instance (in my opinion).