Is one before bar/ bat mitzvah obligated (or allowed) to ask forgiveness for misdeeds, as they are not entirely accountable for them (source needed: that one’s averot are upon the father until the age of bar mitzvah)? Can one ask forgiveness for such deeds after he becomes bar mitzvah?Since the other may likely not even remember the misdeed, perhaps such deeds do not benifit from an apology.
While the child is still a minor:
Minors basically can get away with anything and are technically exempt from all damages they may incur (see for example, this excellent article from the Business Halachah Institute, point 5). The parent may be obligated to make certain restitutions, and general overarching rules of Chinuch may require that the parent insist that the child 'apologize', but there is no direct obligation on the child to apologize (as there are technically no obligations on a minor to begin with).
Regarding a minors' oligation after he becomes an adult:
The Kitzur Shulchan Aruch 165:6 writes:
קָטֹן שֶׁגָּנַב אֵיזֶה דָבָר, אִם הוּא בְעָיִן, מְחֻיָבִין לְהַחֲזִירוֹ. וְאִם אֵינוֹ בְעָיִן, פָּטוּר מִדִינֵי אָדָם אַף לְאַחַר שֶׁיִגְדַּל. אַךְ לָצֵאת יְדֵי שָׁמַיִם, חַיָב לְשַׁלֵם כְּשֶׁיִגְדָּל. וְכֵן אִם עָשָׂה שְׁאָר עֲבֵרוֹת בְקַטְנוּתוֹ כְּשֶׁהוּא בַּר הֲבָנָה, טוֹב שֶׁיְקַבֵּל עָלָיו אֵיזֶה דָבָר לִתְשׁוּבָה. וְעַל זֶה נֶאֱמַר, גַּם בְּלֹא דַעַת נֶפֶשׁ לֹא טוֹב.
If a child steals something, if it is still intact, you are obligated to return it; but if it is no longer intact, he is legally exempt from making restitution even after he becomes of age. But in order to fulfill his obligation before the judgement in Heaven, he must make restitution when he becomes of age. Similarly, if he committed other sins in his youth [before Bar Mitzvah], it is advisable that he accept upon himself some sort of repentance when he reaches an age of understanding. Concerning this it is said, "For the soul to be without knowledge is not good."
We see from this source that while there is no obligation for a person to do Teshuva for an Aveirah they did as a minor, it is considered appropriate and meritorious to do so.
However, it's implied from the Kitzur that it does not need to be the complete Teshuva process (i.e. all the steps involved in a standard Teshuva, including asking forgiveness from the person affected). It seems that a 'token' repentance would suffice for transgressions committed as a minor. Of course, the wording sounds very subjective, and with anything that may have practical applications CYLOR for guidance.