Can a minyan of children under Bar Mitzvah say Kaddish and Kedusha?

Question

If a minyan of children (no adults) are praying, can they recite Kaddish and Kedusha?

At first glance, each child "pretends" to be an adult (well, any praying they do is in preparation of adulthood), so they can make a minyan. Or perhaps not.

Answer 1

In the Sefer called ילדים כהלכה it says that a Minyan of kids under bar Mitzva davening together may not say Kaddish, Kedusha or repeat the Amida. There is no Chinuch involved and they should daven as individuals.

י) מניין של קטנים - אין להניח לקטנים לארגן לבדם תפילה עם חזרה וקדיש וברכו וכו' ללא עשרה גדולים ואין בזה משום חינוך אלא יתפללו ללא חזרה וקדושה וקדיש . ‏

I guess he means that it's wrong Chinuch to teach kids that they can say Kadish and Kedusha without a minyan of adults.

Unfortunately, the online version of the Sefer does not bring primary sources, and I don't have a printed copy handy.

As Double AA pointed out, the אגרות משה - חלק ד in Orach Chaim 98 mentions 2 issues that would make a minyan of children forbidden:

Firstly he proves that it's a Torah prohibition to say Kedusha and Kaddish without a Minyan.

If that were the only problem he would allow it - theoretically - if the children did it of their own accord without any adult help. (I.e. there would be no obligation to stop them making their own Minyan without adult intervention.)

Secondly, he says that repeating the Amida would constitute saying Gcd's name in vain, since it's not a valid repetition.

This is serious enough that they would have to be stopped, even if they initiated the entire Minyan.

Answer 2

Kaddish

See SA OC 55, 1 For Kaddish we need 10 men 13 old and in Sa'if 4 9 + a child is discussed. When you say that ktanim, they need to learn not to count a child (further when they became gdolim). Similarly they don't make alone birkat chamets and remain outside of several mitsvot.

Zimun and Keddusha

To say Kedusha is excluded as you can see below because that in keddusha there is th name of G-d : See Shulchan Aruch Orach Chayim siman 199, 6:

נשים ועבדים וקטנים אין מזמנין עליהם אבל מזמנין לעצמן ולא תהא חבורה של נשים ועבדים וקטנים מזמנין יחד משום פריצותא דעבדים אלא נשים לעצמם ועבדים לעצמם ובלבד שלא יזמנו בשם

Women, slaves and minors (less than 13 years and one day)... they make zimun alone, groups of women alone, groups of slaves alone and groups of minors alone, if they will not pronounce the Name of G-d.

Note:

For Kaddish there is no Name of G-d but as soon in the first paragraph of the answer nothing is mentioned contrarily to Birkat Hamazon. For women I remember someone said me that the daughters of Rav Chisda did recit the Kaddish for him.