Learn Farsi: به دلیل ازدحام شدید، مردم برای عبور کردن یکدیگر را هل می‌دهند. - Due to the severe congestion, people push each other to cross.

You could say ezdehâm chenân shadid ast ke mardom barâye obur kardan yekdigar râ hol midahand (The congestion is so severe that people push each other to cross). The original sentence uses the prepositional phrase be dalil-e (due to) instead of the correlative conjunction.

Is the noun ezdehâm used only for crowds of people, or can it be used for traffic?

It can be used for both. ezdehâm broadly means 'congestion', 'crowding', or 'a swarm'. You will frequently hear ezdehâm-e jam'iyat (crowd of people) as well as ezdehâm-e terâfik (heavy traffic). Here, the adjective shadid (severe/intense) emphasizes how tightly packed the area is.

Why do we need the marker râ after yekdigar?

yekdigar means 'each other' and acts as the direct object receiving the action of the compound verb hol dâdan (to push). Because 'each other' represents a specific, definite group of people being pushed, it requires the definite direct object marker râ.

Could we just say barâye obur instead of using the full infinitive barâye obur kardan?

Yes, absolutely. obur is a noun meaning 'crossing' or 'passage'. Saying barâye obur (for crossing) sounds perfectly natural, is slightly more concise, and is just as common as using the full infinitive obur kardan (to cross) in this context.