Learn Farsi: خواهرت اینجا نیست؟ چرا، اینجا است. - Isn't your sister here? Yes, she is here.

In Farsi, چرا is used to answer a negative question affirmatively. Since the first person asked "Isn't your sister here?" (which uses the negative verb نیست), the second person uses چرا to say "On the contrary, yes she is." If they wanted to agree that she wasn't there, they would say نه (no).

Could I just use بله to say "yes" in this sentence?

If you answered a negative question like this with بله (yes), it would be confusing. In Farsi, replying to a negative question with بله implies you agree with the negative statement (meaning "Yes, you are right, she isn't here"). To contradict the negative and say she actually is here, you must use چرا.

How does the word خواهرت show possession?

The word خواهرت is made of خواهر (sister) plus the ending ـت (your). Adding this short suffix to the end of a noun is the most common way to say "your" (singular informal) in everyday Farsi.

Why does the sentence use اینجا است as two separate words?

Writing اینجا است as two separate words is the formal, standard written style for "is here". In everyday spoken conversation, native speakers almost always blend these two words together into اینجاست to make it flow faster.