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年长的女士
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. 讨论这个问题时, 他们竟然高声争吵起来。
When young, he lived in a very poor mountain village in northwestern China. 年轻时, 他住在中国西北部一个十分贫穷的山村里。
As soon as finished, the job seemed too easy for them. 一旦完成, 这件工作对他们来说似乎太容易了。