Learn Arabic (Modern Standard): هل ينتظر أحد في الاستقبال غير الضيوف الذين عندهم حجز مسبق؟ - Does anyone wait at the reception other than the guests who have an advance reservation?

Because this is an interrogative sentence (which behaves like a negative sentence for exception rules) and the group being excepted from (أحد) is explicitly mentioned, غير can take one of two cases. It can be accusative (غيرَ, ghayra) as the direct exception, or it can act as a substitute (badal) and copy the case of the word it is excluding from. Since the subject أحد is nominative, you can correctly say either غيرَ or غيرُ.

Why must the word for guests (الضيوف) be in the genitive case (majrur)?

Unlike the standard exception particle إلا (illa), the words غير (ghayr) and سوى (siwa) always grammatically act as the first part of an idafa (possessive construction). Therefore, the noun immediately following them is forced into the genitive case because it is the second part of the idafa (mudhaf ilayh). Here it becomes الضيوفِ (al-dhuyuufi).

Why do we use the relative pronoun الذين here?

الذين (who/which) is the masculine plural relative pronoun. It is used here to agree with الضيوف (the guests), which is treated as a rational (human) plural. Remember that if the plural noun were non-human, you would use the feminine singular relative pronoun التي instead.

In the phrase عندهم حجز مسبق, what case is حجز (reservation) and why?