Learn Farsi: هم‌اتاقی من دانشجو است. - My roommate is a university student.

The prefix ham- means "same" or "mutual". When added to otâgh (room), it builds a compound concept. To make it refer to a person, we add the suffix -i. So, ham-otâghi literally means "someone who shares the same room", which translates to "roommate".

Is ham- always attached directly to the noun without a space?

In modern written Farsi, it is very common to use a half-space between ham- and the noun, as seen here in هم‌اتاقی. This keeps the prefix visually distinct from the main word without completely breaking it into two separate words.

I see an Ezâfe is needed between ham-otâghi and man. How is it pronounced since ham-otâghi ends in a vowel?

Because ham-otâghi ends in the long vowel -i, you must add a "y" sound to bridge the words. You pronounce the phrase as ham-otâghi-ye man.

Could I use dâneshâmouz instead of dâneshjoo in this sentence?

You could, but it changes the meaning slightly. dâneshjoo specifically means a university student. If your roommate is in high school or younger, you would use dâneshâmouz instead.