What actions invalidate the Hajj, and do quarreling and فسوق (transgression/disobedience) invalidate it, and is the Hajj recorded for a person as they performed it, along with the mistakes or quarrels that occurred during it?

Hajj is not invalidated except by sexual intercourse during the state of ihram (definition), and this is what the people of knowledge have agreed upon. As for the "rafath" (sexual intercourse) forbidden in the Quran, it refers to sexual intercourse. Disputation and transgression (sins) do not invalidate Hajj, but they do affect the pilgrim's reward and may deprive the doer of the reward of an accepted Hajj.