Learn Turkish: Misafiriniz aç mı? - Is your guest hungry?

The suffix -iniz means "your" when you are talking to multiple people or being polite and formal to one person. If you were talking to one friend informally, you would say misafirin.

Does misafiriniz mean "your guests" or "your guest"?

It means "your guest" (just one). The -iniz part tells us who the guest belongs to (plural or formal "you"), but the guest itself is singular. If you wanted to say "your guests", you would add the plural suffix -ler first, making it misafirleriniz.

Where is the word for "is" in this sentence?

In Turkish, there is no direct word for "is" when talking about a third person or object in the present tense. You just put the subject (misafiriniz) and the adjective (aç) together, and the "is" is naturally understood.

Why is the question particle mı instead of mi?

The question word follows 4-way vowel harmony based on the word right before it. Since the only vowel in aç is a, the question particle takes the undotted ı to become mı.