Learn Russian: Восьмой участник — студент, а девятый? - The eighth participant is a student, and the ninth?

Ordinal numbers in Russian act just like adjectives. Because they describe the masculine noun участник (participant), they take masculine adjective endings. The ending is -ой when the stress falls on the last syllable (like in восьмой), and -ый when the stress is elsewhere (like in девятый).

Why is there no noun after девятый?

Just like in English, you do not have to repeat the noun if it is obvious from the context. Девятый refers back to участник, so it stays in the masculine Nominative form even though the noun itself is left out.

Why is there a dash between участник and студент?

Russian drops the present tense verb for is or are. When a sentence simply states that one noun is another noun (the participant is a student), Russian writers often use a dash to show exactly where the verb was skipped.

The English translation uses the word and, so why does the Russian use а instead of и?

The word и simply adds things together, but а is used to show contrast or a shift in focus. Because the sentence shifts attention from one person (the eighth) to ask a question about someone else (the ninth), а is the natural choice.