What is the relationship between the five prerequisites (Islam, Sanity, Puberty, Freedom, Ability) and the validity (Sihhah) and fulfillment (Ijza') of Hajj?

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Islam and Sanity are prerequisites for both obligation and validity; thus, Hajj is not obligatory upon nor validly performed by a non-believer or an insane person, as they are not people of worship. Puberty and Freedom are prerequisites for obligation and fulfillment, but not for validity; therefore, if a minor or a slave performs Hajj, their Hajj is valid but does not fulfill the obligatory Hajj of Islam. Ability (Istita'ah) is a prerequisite only for obligation. If one who is unable undertakes the hardship, travels without provision or means of transport, and performs Hajj, their Hajj is valid and fulfills the requirement, similar to someone who forces themselves to stand or fast when excused from doing so.