Learn Arabic (Modern Standard): الزميل أستاذ قديم.

In Arabic, simple "is/are" sentences do not use a verb in the present tense. Instead, you just place the subject (like الزميل, the colleague) right next to the information about it (أستاذ قديم, an old professor).

If I wanted to ask "Who is the colleague?" to get this sentence as an answer, which question word would I use?

You would use من (man), which means "who". The question would be من الزميل؟ (Who is the colleague?). Remember to use من when asking about people, and save ما (maa) for things or ideas.

Why does قديم come after أستاذ, and why doesn't it have "al-" (ال) attached to it?

In Arabic, adjectives always come after the noun they describe. The adjective also has to match the noun's "definiteness" (whether it has "the" or not). Since أستاذ (a professor) is indefinite and doesn't have ال attached to it, the adjective قديم (old) must also be written without it.

Does قديم mean the professor is an elderly man?

Not necessarily! The word قديم is generally used for things that are old (like an old book) or situations that go way back in time (like a long-time colleague or a former professor). If you wanted to specifically say he is an elderly man, you would usually use the word كبير (kabiir), which literally means "big" but is used for age.