Your second sentence, "She advocates for change to be made," is more correct. Although the second sentence would be understood in conversation, in English, the subjunctive is primarily used after specific trigger words or phrases (suggest, demand, recommend), which do not include "advocate." As for your last question, the word "that" triggers a conjugated verb, so "to be" is incorrect, and "will be" implies that the changes are certain, which I do not believe fits with the meaning of your sentence. To make the sentence more communicative, I would rephrase the sentence to one of the following, depending on context: "She is an advocate for change." "She advocates (for) change." "She recommends that changes be made."