An elderly man had collapsed while crossing the street, ... (Para. 1)
Meaning: An old man had fallen to the ground and lost consciousness while he was crossing the street.
elderly, old or senior: when we speak of people, we may use either "old" or "elderly" or "senior"; when speaking of places or objects, we tend to use "old" only. Please compare:
an old church古老的教堂
an old / elderly lady年長的女士
Notice that "elderly" is a polite way of saying "old", and "senior" is the best way usually.
Please also pay attention to the "while"-clause. The subject and the verb "be" can be omitted. Here in the text "... while he was crossing the street" is shortened to ".... while crossing the street". Some other conjunctions indicating time or condition can also be used in this way. Please read:
While discussing the matter, they started to argue in a very loud voice. 討論這個問題時, 他們竟然高聲爭吵起來。
When young, he lived in a very poor mountain village in northwestern China. 年輕時, 他住在中國西北部一個十分貧窮的山村里。
As soon as finished, the job seemed too easy for them. 一旦完成, 這件工作對他們來說似乎太容易了。