How can a boy become bar mitzvah before his older friend?

A child born during Adar Sheini on a leap year becomes bar mitzvah on the same date of the regular Adar during a standard year. Therefore, if two children were born on the same leap year--one on a later date in Adar Rishon and one on earlier date in Adar Sheini--the younger child will become bar mitzvah before the older one (in a standard year).

[סעיף י]

Does the Date Line play a role in determining bar mitzvah?

The poskim disagree on how to determine the bar mitzvah date of a child who comes of age in a location across the International Date Line from where he was born. For example, if he was born in the United States on aleph Nissan and came of age in Australia, there is a question about whether he should become bar mitzvah on his birth date (even though it is still a day earlier at his place of birth) or whether he should wait another day. Some hold that his present location is the determining factor, while others hold that his birthplace should be considered under certain circumstances.

ביאורים ומוספים דרשו, 57

Can a secular person be counted in a minyan?

A mumar--one who sins out of spite, serves Avodah Zorah or desecrates the Shabbos--cannot be counted in a minyan. A person who denies the validity of Torah Sheba’al Peh may not be included in a minyan either. A tinok shenishba--a child who was captured by non-Jews and never had any exposure to Judaism in his youth--is not held responsible for his actions and is not considered a mumar. He may count for a minyan. Contemporary poskim debate whether modern-day secular Jews fall into the category of tinok shenishba. Some are more stringent in Eretz Yisroel, where there is more exposure to Torah and mitzvos.

ס"ק מו-מז; ביאורים ומוספים דרשו, 59-5

• If one of the ten men in shul starting davening on his own, the chazan may still say Kaddish. As long as there are ten men there, they will be joined by the Shechinah and a davar shebekedusha can be said. Most Achronim are lenient even if there are up to four people who are not responding to Kaddish.

• A shoteh who is exempt from mitzvos cannot be counted for a minyan. The Gemara gives specific examples of what constitutes a shoteh. A person who does not have any of those characteristics but is regarded by others as mentally challenged can count towards a minyan as long as he understands that there is a Hashem who commanded us to do mitzvos.

• L’chatchilah, there should be at least two members of the minyan who answer Amen to Kaddish. This is because Kaddish ends with the words v’imru Amen (“and they will answer Amen”). If everyone in the minyan wants to recite Kaddish (instead of responding to it), however, they may be lenient. 

• Can a person standing behind a room divider be counted in a minyan?

• Can a person standing in the ezras nashim be counted in a minyan?

• Can people in two different rooms be counted together for a minyan?