Learn Farsi: دخترک یک قالیچه داخل اتاق می‌گذارد. - The little girl puts a small rug inside the room.

The suffix -ak is a diminutive. It usually means "little" or "small," so dokhtarak literally means "little girl." Depending on the context, it can also add a feeling of affection or sometimes even pity, though here it simply means she is young or small.

Why does the word for rug (ghali) use the suffix -che (ghaliche) instead of -ak?

Both -ak and -che are diminutives used to make things smaller, but they attach to different words by convention. -che is very commonly used for inanimate objects and places (like baghche for "small garden"). ghaliche is the standard, fixed word for a small rug; saying ghali-ak would sound unnatural.

Since the translation says "a small rug," why isn't there an indefinite -i at the end of ghaliche?

In formal and written Farsi, using the number yek (one/a) before the noun is enough to show it is indefinite. You will often hear people use both together in everyday speech (like yek ghaliche-i), but grammatically, just yek does the job perfectly on its own here.

Is there an invisible Ezafe connecting dakhel (inside) and otagh (room)?

Yes! When using spatial nouns like dakhel (inside), (outside), or (under) as prepositions, you need an Ezafe to connect them to the following noun. So it is pronounced .