彼女は何が起きたかまるで気にしていないかのように行動した。

English Translation

She acted as if she didn’t care what happened.

Could 気にしていない be replace with one of
気にしていなかった、気にしなかった、気にしない ?

Before taking your question, let me point out that the original Japanese sentence sounds unnatural a bit and very wordy although understandable. My alternative translation is:

彼女は事態を気にも留めない素振りをみせた。

What makes the original Japanese sentence awkward is:

  • 行動した in this particular context is closer to “to make a move” (e.g. she changed her previous posture, and took a new initiative). There is no such a strong nuance in the English sentence. She might just keep calm. So, replace 行動する with 素振り(そぶり)をみせる. “Behavior” in English is 振舞い(ふるまい), so you can get the connotation of 振る (lit. to swing). – Our ancestry wore Kimono(着物)with long sleeves. They danced elegantly by swinging the long sleeves. 素振り (attaching 素 = pure or spontaneous) means "behaviors or postures that can be observed from one’s facial expressions or body gesture). So, 素振りをみせる bears the meaning of “as if” and also “behavior”

  • 何が起きたか is a word-for-word translation from “what happened” in English, but 何が起きたか is a bad collocation with 気にしない because 何が起きたか also means “what happened? I don’t know”. 気にしない is “don’t care”, so the person exactly knows what happened, and then intentionally ignores the fact. The original Japanese translation is logically confusing. 事態(じたい) from my translation means “situations”.

  • 気にしていない is okay but 気にも留めない(とめない) is much better. 気に留める is closer to “keep/bear in mind”. 留 means “to retain”, “to store” or “to be stuck”. So, 気にも留めない is an intentional act whereas 気にしていない can also include unintentional one (i.e. not aware of it).

Back to the question from ericaw

  1. 彼女は何が起きたかまるで気にしていなかったかのように行動した。-- “She took a move as if she HAD not BEING caring what HAD happened.” (i.e. there is a time gap between something happened and her actual action.) It makes more complicated and even misleading than the original Japanese sentence.
  2. 彼女は何が起きたかまるで気にしなかったかのように行動した。-- “She took a move as if she HAD not cared what HAD happened.” I don’t recommend this either.
  3. 彼女は何が起きたかまるで気にしないかのように行動した。-- “She took a move as if she TRIED not to care what happened.”

As explained, the original Japanese sentence is not good enough that replacing a single word doesn’t improve the flaws.