I think if you combine the two answers, you get the right one : les choses que j’aurais faites avec cet argent.
J’aurais in conditional as you note - probably a typo in the answer given;
agreement of “ faites “ with plural, feminine direct object ( les choses) preceding the verb, as per the answer given.
Special cases when the past participle agrees (in number & gender) when used with 'avoir' in Le Passé Composé%252Fsearch%253Fs%253DQue%252Bagreement
Happy to be corrected if I have this wrong.
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