Q 1: Is swearing by anyone or anything other than Allah (the Most Exalted) basically considered major Shirk (associating others with Allah in His Divinity or worship that takes the Muslim out of Islam) unless it includes something that renders it minor Shirk (associating other partners with Allah that is not tantamount to taking the Muslim out of Islam)?What does the Prophet (peace be upon him) mean by saying, Whoever amongst you swears, (saying by error) in his oath 'By Al-Lat and Al-`Uzza', then he should say, 'La ilaha illa Allah (there is no god but Allah)'? And what is the rank of this Hadith? (Part No. 1; Page No. 131

Swearing by anyone or anything other than Allah is basically minor Shirk unless those who do so intend to give what they swear by the same rank as Allah concerning glorification and exaltation. In such a case this is considered major Shirk.The Prophet (peace be upon him) ordered that "La ilaha illa Allah" should be said by whoever swears (by mistake) by Al-Lat and Al-`Uzza, which were two of the Arab's idols worshipped besides Allah, because swearing by Al-Lat and Al-‘Uzza contradicts the word of Tawhid (Monotheism) if it is intended to glorify Al-Lat and Al-‘Uzza in the same way of glorifying Allah. If swearing by them is not intended to glorify them, then this is against the perfection of Tawhid, and whoever swears by them, he indeed glorifies them. Whoever swears by idols and the like, his oath is not considered valid but he should seek forgiveness from Allah and say "La ilaha illa Allah" and no expiation is due on him. The word of Tawhid annuls any kind of association with (anything or anyone) other than Allah, and it acquits those who say it from Al-Lat and Al-`Uzza and every other false deity but Allah. This word essentially means that there is no one that has the right to be worshipped but Allah; so it emphasizes worship of Allah and denies such a right to anyone but Allah. Consequently, if a person says it from the depths of his heart out of loyalty to Allah coupled with true repentance to Him for what he has said, such a sin will be expiated.The Hadith mentioned in the question is authentic and it was related by Al-Bukhari and Muslim in their Two Sahih (authentic) Books of Hadith and also related by Al-Bayhaqy in his Sunan. The wording of the narration of Al-Bukhari from Abu Hurayrah (may Allah be pleased with him) is thus: (Part No. 1; Page No. 132)  Whoever takes an oath in which he mentions Al-Lat and Al-`Uzza (forgetfully), should say 'la ilaha illa Allah (None has the right to be worshipped but Allah),' and whoever says to his companion, ‘Come along, let us gamble' must give alms (as an expiation).