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In Artscroll’s edition of Sefer HaChinuch (vol. 2, p. 303), they quote a discussion regarding whether women are exempt from davening Mussaf:

If women are obligated as men are in all the communal offerings, there is a reason to obligate women in the Mussaf prayer, since it is representative of the Mussaf offering in which women are obligated. Thus, the question of whether women must recite the Mussaf prayer today is contingent upon the question of whether they are included in the obligation of all the communal offerings, and that they are therefore exempt from reciting the Mussaf prayer (see Teshuvos R’ Akiva Eiger §9, and R’ Akiva Eiger on Shulchan Aruch, Orach Chaim 106:2).

(Artscroll spends the rest of the piece addressing how this opinion interprets Ben Buchri’s opinion that Kohanim and Leviim are exempt from the Shekalim in light of the fact that Sukkah 53a indicates that they davened an obligatory Mussaf.)

I see also that Mishnah Berurah 106:4 cites the Tzlach (Artscroll ad. loc. references Tzlach to Berachos 26a without actually quoting him) as saying similarly that women are exempt, without quoting a reason; I don’t have access to this Sefer to see his reasoning inside.

According to these opinions, that women are exempt from Mussaf due to their being exempt from the Shekalim, would the same hold true for the other groups of people exempt from Shekalim, i.e. children under 20¹ and slaves? (I ask more about the children, as in general slaves are liable and exempt in the same Mitzvos as a woman.)

¹I base this statement on the Bartenura to Shekalim 1:3:

וקטנים. אפילו הביא שתי שערות והוא פחות מבן עשרים:

”And minors” - even if he has produced two hairs and is younger than 20.

And Yachin ad. loc.:

וקטנים כל שהוא פחות מבן עשרים קרוי קטן, ואפילו הביא ב' שערות.

”And minors” - anyone younger than 20 is called a minor, even if he produced two hairs.

However, I see that the Rambam ad. loc. understands this exemption differently:

וקטן שלא הביא שתי שערות אין ממשכנין אותו אלא שמניחין אותו ואם נתן מקבלין מידו אמרו אין ממשכנין עד שיביא שתי שערות

And a minor who has not produced two hairs, we do not take collateral from him, but rather we leave him. If he gave, we will accept from his hand. They said: we do not take collateral until he produces two hairs.

Obviously my question can only apply if children ages 13-20 are exempt from Shekalim, as children under 13 are exempt from Mitzvos anyway.

R. Baruch HaLevi Epstein in Torah Temimah to Shemot 30 footnote 22 writes that according to the opinion which you cited that would exempt women from tefilat musaf (which he attributes to Besamim Rosh and subsequently R. Akiva Eger) and according to the many opinions that a young man from thirteen to twenty years of age was exempt from the obligation to donate a half-shekel (Bartenura, Chinuch, Rokeach, Gra), then it would indeed appear that a boy under twenty would be exempt from tefillat musaf, to the extent that he would not be able to pray musaf as a shatz in order to allow the congregation to fulfill their obligation.

However, he concludes

והוא דבר חדש ונפלא מאד וצ"ע רב

This is something new and very astounding, and requires much thought.

This may very well depend on the reason for women's exemption from mussaf. R. Akiva Eiger (both in the teshuvah and in the commentary to Shulchan Aruch) cites the Besamim Rosh as linking their exemption to their lack of involvement in the korbanos. However, in the commentary to Shulchan Aruch he also cites the Tzlach's explanation. This is what the Tzlach says (Berachos 26a):

ומדברי התוס' למדתי כונה אחרת רמוזה בלשונם שכתבו משום שהיא תדירה בכל ולכאורה מלת בכל אין לה הבנה שהיה להם לומר שהיא תדירה בכל יום או בכל זמן ולכן אני אומר שכיונו במה שאני מסתפק אם תפלת המוספין נוהגת בנשים שהרי היא מצוה שהזמן גרמא ואף שהתפלה אין מן התורה רק מדרבנן הרי לדעת התוס' לעיל דף כ' ע"ב גם במצות דרבנן שהזמן גרמא נשים פטורות אלא שבתפלה חייבינהו רבנן כיון דרחמי נינהו כמבואר לעיל והיינו בשלש תפלות הקבועות בכל יום ואפי' בשבת וי"ט שהם רק שבח מ"מ כיון דבחול רחמי נינהו לכן לא חילקו בין שבת ויו"ט לחול וכמ"ש רבינו יונה כאן לענין תשלומין בתפלה שאחריה אבל תפלת מוסף שאיננה רחמי כמבואר ברבינו יונה כאן דלכך אין לה תשלומין והיא מצות עשה דרבנן שהזמן גרמא ודאי דנשים פטורות לדעת התוס' וא"כ זהו כוונת התוס' שהקדים תפלת המנחה למוסף משום שהיא תדירה בכל ותרתי קארי למעליותא דמנחה חדא שהיא תדירה ועוד שהיא נוהגת בכל באנשים ונשים משא"כ מוסף שאינה תדיר ואינה נוהגת בנשים

And from the words of Tosafos I derived another intent hidden in their language, for they wrote "that it is frequent in everything". And seemingly the word[s] "in everything" have no understanding – they should have said that it is frequent every day, or every time. And therefore I say that they intended that which I was unsure about, if the mussaf prayer is practiced by women since it's a time-bound positive commandment. And even though prayer is not [a] biblical [commandment] but only rabbinic, according to the opinion of Tosafos above on 20b women are even exempt from rabbinic commandments that are time-bound, except that the Sages obligated them in prayer since it is [requesting] mercy as explained above. But that is only with [regard to] the the three daily set prayers, and even on Shabbos and holidays when [the prayers] are only praise but since on weekdays they are [requests for] mercy [the Sages] did not make a distinction between Shabbos/holidays and weekdays, as Rabbeinu Yonah writes here with regard to making up [a prayer] with the next prayer. But [with regard to] the mussaf prayer which is not [a request for] mercy – as is clear from Rabbeinu Yonah here since that is why there is no makeup – and it is a rabbinic time-bound positive commandment, women are certainly exempt according to the opinion of Tosafos. And if so, this is the intent of Tosafos: that [the Mishnah] mentions minchah before mussaf because it is frequent in everything, and minchah has two advantages 1) it is frequent 2) it is practiced by everyone – men and women. Whereas mussaf is not frequent and it is not practiced by women.

According to this women's exemption has nothing to do with korbanos so it would be hard to extrapolate to other people who are similarly not involved in korbanos. (and of course the Besamim Rosh is of dubious value.)