In this teshuva, Rav Yosef works out an interesting distinction regarding the law of a minor being called up to read the haftara, and specifically with regard to parashat zachor. He cites Rabbeinu Tam, who rules that a minor cannot be called up for any aliyah from a second Torah, since that second Torah represents a different obligation for the congregation, and since the minor is not obligated, he cannot discharge the obligation of others. However, the Mordechai and others hold that a minor can be called up for maftir on such days, since the Gemara in Megilla says that a minor can even be called up for one of the regular seven aliyot.
However, when it comes to parashat zachor, it seems fairly clear that a minor cannot be called up, since it is generally considered to be a d'oraita obligation, and the minor is definitely not obligated. This may apply to parashat Parah as well, although its status as a d'oraita law is not as clear.