Learn Farsi: بقیه در خانه هستند.

Yes! While kasi means 'someone' and chizi means 'something', baghiye means 'the rest' or 'the others'. It acts as a pronoun here because it takes the place of a specific group of people or things that were already mentioned.

Why is the verb plural (hastand) if baghiye is a single word?

Just like in English where we say 'the others are', Farsi treats baghiye as plural when it refers to a group of countable people or objects. If it referred to something uncountable (like 'the rest of the food'), it would take a singular verb. Here, it means 'the other people', so we use the plural hastand.

Can I add a noun after baghiye to be more specific?

You absolutely can! You just need to connect them with the ezafe (the connecting 'e' or 'ye' sound). For example, baghiye-ye mardom means 'the rest of the people'. But in this sentence, it works perfectly on its own as a pronoun.

Do I always have to use dar (in/at) when saying someone is at home?

In written or careful Farsi, yes, dar khāne is standard. However, in casual everyday speech, Iranians often drop the dar entirely and just say baghiye khāne hastand (or even more casually, baghiye khunan).