How can a Muslim ensure meeting Allah with no arrogance or polytheism in their heart, and does the presence of an atom's weight of arrogance or polytheism unknowingly necessitate eternal damnation in Hell?

Arrogance is the rejection of truth and the contempt of people. It is the refusal of truth and the disdain of people. No one who has a mustard seed's weight of arrogance in their heart will enter Paradise. As for the shirk (polytheism) that the Prophet, peace and blessings be upon him, feared for his Ummah, it is ostentation (riya'), which is the minor shirk, and it is more subtle than the creeping of an ant. To get rid of arrogance and ostentation, one must recognize them and realize their danger, strive against the self to abandon them, accept the truth, be humble, respect people, and frequently recite the supplication: "O Allah, we seek refuge in You from associating anything with You knowingly, and we seek Your forgiveness for what we do not know." Eternal dwelling in Hellfire is for those who commit major shirk that expels them from the fold of Islam. As for arrogance and minor shirk, they are among the major sins for which their perpetrators may be punished and then enter Paradise if they do not repent or if Allah does not forgive them.