Learn Turkish: Genç bir kişiye oranla yaşlı birinin metabolizması daha yavaş. - Relative to a young person, an old person's metabolism is slower.

Yes, oranla and kıyasla are interchangeable here. They both mean "compared to" or "relative to" and require the preceding noun to be in the dative case. That is why kişi (person) takes the dative suffix -ye, becoming kişiye.

Why is it yaşlı birinin instead of just yaşlı bir kişi?

The sentence uses biri (someone or one) as a pronoun to avoid repeating the word kişi. Because we are talking about an old person's metabolism, it forms a possessive phrase. Biri takes the genitive suffix -nin to show ownership, and metabolizma takes the possessive suffix -sı.

Why is the word order Genç bir kişi rather than Bir genç kişi?

In Turkish, when a noun is modified by both an adjective and the indefinite article bir, the adjective almost always comes first. The standard structure is Adjective + bir + Noun, making it Genç bir kişi.

There is no verb at the end of this sentence. Is it implied?

Yes, the "to be" verb is implied. Daha yavaş simply means "is slower" here. You could add the formal copula suffix -tır to the end (daha yavaştır) for a more factual or scientific tone, but in everyday communication it is perfectly natural to leave it off.