Is what was mentioned in the question—regarding answering a requirement that involved assuming the placement of an idol for worship, or thinking boastfully upon academic excellence, or specific actions during a morning assembly at a non-Muslim school like closing one’s eyes or looking at a single spot—considered polytheism (shirk) or disbelief (kufr)? And does the hadith, “Indeed, Allah has pardoned for my Ummah their mistakes, their forgetfulness, and what they are coerced into,” apply to these cases?

A Muslim woman must worship Allah alone and not take idols, and she must declare this if asked about her deity, except in the case of coercion to utter disbelief.

Studying in non-Muslim schools is not permissible if it calls for concealing one's religion or declaring disbelief, unless she openly declares her Islam and is allowed not to participate in their rituals, or if she is concealing her Islam from her Hindu family.

It is obligatory to avoid sitting with those who mock the verses of Allah or disbelieve in them, and it is not permissible to conceal Islam to avoid drawing attention.

If the question is about past actions, then repentance from them is obligatory, and one must accustom oneself to disavowing polytheism and its people.