1) Can I be yotzai mishloach manos or matanos l’evyonim by giving to a katan?
2) Do a chasan and kallah fast on taanis esther during the week of sheva brachos?
1) One cannot fulfill the mitzvah of mishloach manos by giving to a katan, because the mitzvah requires giving to a bar chiyuva, somebody who is obligated in the mitzvah, and a katan is not obligated in the mitzvah.
This ruling is given by a number of authorities, including the Ben Ish Chai (Tetzaveh 16), Ashrei Ish (citing from Rav Elyashiv, p. 312), and others. Although Shut Vayomer Boaz (331) writes that the mitzvah is fulfilled with older children, he concludes by writing that he has heard that the mitzvah is not fulfilled.
Concerning matanos la-evyonim, however, the same poskim write that the mitvzah is fulfilled by giving to children who appreciates (understands) the giving.
See Ki Va Mo’ed (p. 88 and p. 118) for further sources.
2) A chasan and kallah don’t fast for taanis esther during the week of Sheva Brachos. See Kitzur Shulchan Aruch 141:2, who writes that the do not have to fast, but adds that they should ‘pay back’ the fast another time; see also Maharsham 4:148; Divrei Yatziv, Orach Chaim 2:291; see also Mishnah Berurah 686:16, who only mentions a chasan on the day of his wedding.