Learn Russian: Пятьдесят процентов клиентов сделали заказ. - Fifty percent of the clients made an order.

This is because of the number пятьдесят (fifty). In Russian, numbers ending in 5 through 9, as well as 0 (like 10, 20, 50), require the noun that follows them to be in the Genitive plural.

Why is клиентов also in the Genitive plural? Does the number 50 affect it too?

Not directly. Клиентов is in the Genitive case because it expresses possession or origin, meaning of the clients. Russian often chains Genitive nouns together. Literally, this translates to fifty [of] percents [of] clients.

The subject starts with a number. Why is the verb сделали in the plural instead of neuter singular?

When a subject is a quantity plus a noun, the past tense verb can sometimes be neuter singular (which would be сделало here). However, when the noun refers to living people who are actively doing something—like clients making an order—Russian strongly prefers the plural verb (сделали).

Why doesn't the direct object заказ change its ending here?

Заказ (order) is a masculine, inanimate noun. When an inanimate masculine noun is the direct object of a sentence (in the Accusative case), its ending doesn't change. It looks exactly like its dictionary form.