Alay asked: “If a human develops skills (such as languages, music, sport etc…) in this life and is reborn in the animal realm, does the gandhabba carry any of these “skills” to the next life?”
Yes. Such skills are maintained as one’s gati. Of course they manifest only when one is reborn again in the human realm. An animal cannot display musical talents, if we are talking about musical talents. However, it is possible that the animal may have liking to listen to music, for example.
“Let’s say after many, many life times as an animal, this being is reborn as a human. At this point, would this human still have the ability to be more proficient with the skills that he/she excelled in a past life?”
Yes. That is exactly right. That is why we have heard so much about “child prodigies”: A little kid who can play piano like a pro, a child who can pickup advanced mathematics easily, etc.