Learn Arabic (Modern Standard): أي حارس أزعجك؟

Yes! Unlike fixed (mabni) question words such as من (who) or ما (what), أي is fully declinable. Because it is the subject of this sentence, it takes the nominative case ending with a damma, making it أيُّ (ayyu).

What grammatical rule determines the case ending of حارس in this sentence?

The word أي always forms an idaafa (genitive construction) with the noun that follows it. Because it is the second part of the idaafa, حارس must be in the genitive case. Since it is indefinite, it takes a double kasra (kasratayn), pronounced as حارسٍ (haarisin).

Why does the past tense verb أزعجك start with an alif?

The verb أزعج is a Form IV verb, which is characterized by adding an alif with a hamza to the beginning of the three-letter root ز - ع - ج. Unlike Form I past tense verbs, Form IV verbs always begin with this prefix. The attached pronoun ـك at the end is the direct object meaning "you".

If we were asking about a female guard, how would this sentence change?

You would use the feminine noun حارسة and conjugate the verb for a female hidden subject: أزعجتك (she bothered you). The sentence becomes أي حارسة أزعجتك؟. Note that the word أي can remain exactly the same, although you will sometimes see the feminine form أية used instead.