Katan
11. Katan being motzi a gadol. According to the Magen Avrohom, a chinuch-aged child [who did not daven (דרך החיים הובא שער הציון סק''ב, חזו''א סי' כ''ט סק''ה); or, according to others, even if he already davened (חיי אדם, שו''ת רע''א מהדו''ק סי' ז') ] can be motzi a gadol who already davened since the gadol’s chiyuv to make Kiddush over a cup of wine is only derabanan (מג''א שם סק''א). According to the Minchas Chinuch and others however, he may not (מ''ב שם). Thus, a katan cannot be motzi a woman since someone who is chayav derabanan cannot be motzi someone who is chayav deoraisa (מ''ב שם).
12. 13-year-old who was not checked for simanim. A thirteen-year-old cannot yet grow a beard may not be motzi someone his age since perhaps he did not bring shtei saaros and the other one brought shtei saaros and is certainly a gadol (הגרשז''א, שש''כ פנ''א הערה כ"ו). However, he can be motzi a man or woman who already davened since that is a double safeik (מ''ב ס ק"ג). The same is true with a group of bas mitzvah aged girls.
13. Chinuch-aged boys and girls below bar/bas mitzvah can be motzi one another in Kiddush if they have not yet been yotzei their chiyuv (מג''א סי' קצ''ט סק''ז).
