Learn Farsi: مهمان‌خانه‌ی دانشگاه برای مهمان‌ها آماده است. - The university's guesthouse is ready for the guests.

The suffix گاه means 'place of'. It attaches to nouns or verb stems to create a location. Here, دانش (knowledge) + گاه (place) creates دانشگاه (university, or 'place of knowledge'). You will also see this in words like ایستگاه (station/place of stopping) or آزمایشگاه (laboratory).

Is خانه in مهمان‌خانه acting as a suffix here, or is it just the word for house?

While خانه literally means 'house', it acts as a highly productive suffix in Farsi derivational morphology to create words for specific buildings, businesses, or institutions. مهمان (guest) + خانه becomes مهمان‌خانه (guesthouse or inn). Other common examples include کتاب‌خانه (library) and داروخانه (pharmacy).

Why is there a ی added to the end of مهمان‌خانه‌ی?

This is the written form of the Ezafe particle connecting 'guesthouse' to 'university'. Because مهمان‌خانه ends in a silent 'heh' (ه) which produces an 'e' or 'a' vowel sound, Farsi requires a consonant bridge to connect it to the Ezafe. A ی is added in writing and pronounced as a 'ye' sound, making it 'mehmān-khāne-ye dāneshgāh'.

Since مهمان‌خانه already contains the word for guest (مهمان), does it sound repetitive to use مهمان‌ها later in the sentence?