Can't discern how a set of clauses function
外交部发言人耿爽14日就两名中国公民在日本不幸遇害答记者问时……


It is not easy to understand a long sentence.
But, we can simplify it.

外交部发言人耿爽 (title + name) can be simplified as 他, he.

The date, 14日, is not important here, so we omit it for simplification.

两名中国公民在日本不幸遇害 is an event, so we use "the event", 该事件.

We use "the/his/her/their question", 其问, to represent 记者问.

The sentence then becomes 


  他就该事件答其问时……


(Don't you think it is much easier to interpret it now?
I suggest you using this method next time, when you read a looooong sentence.)


  When he answered the question regarding the event, ......


As you mentioned, 就 means regarding, in regard to, with regard to, etc.

Can't we use to or for?
When he answered the question to the event, ......
When he answered the question for the event, ......



If we want to use another Chinese characters to replace 就, the most common one would be 对.

Consider the following two phrases/sentences.

就事论事。
对事不对人。

Here, 就 ＝ 对.

Because we are used to them, it is not good to swith them.
But, the meaning is the same, and we can accept it.

对事论事。
就事不就人。


  他 对 该事件答其问时……
  外交部发言人耿爽14日 对 两名中国公民在日本不幸遇害答记者问时……