1. Question: Why can a child technically read from the Torah for everyone else but cannot blow shofar for everyone on Rosh HaShana?
Background:
A. A person who has a rabbinic (lesser) obligation can’t help perform a mitzvah for someone else who has a Torah (higher) obligation.
B. Shofar is a Torah obligation for an adult. Torah reading is a rabbinic obligation from the prophets which is treated like a Torah level obligation according to the Turei Zahav in Megillah 5b. A child only has a rabbinic obligation in all mitzvos to teach them how to fulfill the mitzvah.
C. A maasah mitzvah, an action of an obligatory mitzvah must be accomplished to fulfill and to help others fulfill the mitzvah of shofar.
D. The mitzvah of reading from the Torah is for people to hear words of Torah.
Answer: By shofar, since the child isn’t obligated on a Torah level then his action of blowing isn’t considered an obligatory mitzvah action therefore he cannot help others fulfill the mitzvah, since his action isn’t a maasah mitzvah, an action of an obligatory mitzvah. But all that is needed by reading the Torah is for words of Torah to be heard and that is being done whether the child has the same level of obligation as the adult or not, therefore he can read from the Torah and others can fulfill their obligation by listening to him.