These しまう doesn't mean the same. 何故気にしてしまうのですか。= Why do you end up caring (/minding)? (though you don't have to do that) This ~てしまう means "end up ~ing", "find oneself ~ing", "can't help ~ing", "against one's will", etc. 昼ごはんまでにレポートを書いてしまう。 漢字の宿題はもうやってしまった。 These しまう are one of the uses of "perfect". (the first one is "future perfect" and the second one is "past perfect / pretérito perfecto") It is used for something that will have/ has/ had been finished. 昼ごはんまでにレポートを書いてしまう。 = I will have finished writing the report until lunch. (If it expresses only ones will, it would be, simply, "I will finish .... ".) (Como "habré terminado..." o "terminaré ... ") 漢字の宿題はもうやってしまった。= I've already finished my homework of kanji. (Como "ya he terminado...") I hope this was helpful.

1「しまう」means "doing it unwillingly" 2&3 complete writing , fininsh homework's completely 「おえる」「とげる」は同じ意味です。例「しおえる」「やりとげる」