What is the reason for the variation in pronouns in Verses 78-80 of Surat Al-Kahf, between the singular "أعيبها" (I should damage it), the plural "فخشينا" (so we feared), and the singular absent "أراد ربك" (your Lord intended), despite all actions referring to the righteous man and the intention belonging to Allah?

The three verbs mentioned in the question: "I intended," "so we feared," and "He intended," do not all refer back to the righteous man. The two verbs "I intended" and "so we feared" refer to him, while the verb "He intended" in Allah Almighty's saying: "And your Lord intended" refers to Allah Almighty. This is due to the eloquence of the Holy Quran, for attributing the intention for the orphans to reach maturity to Allah Almighty is evidence that none but Allah can ordain that. Whereas attributing the act of causing a defect in the ship to the righteous man is evidence that it is within human capability. This exemplifies the etiquette of attributing good to Allah and evil to creation.

As for the reason for using a singular pronoun at one time and the pronoun of majesty (the plural "we") at another time when referring to the righteous man, it is, as Ash-Shawkani mentioned, that Al-Khidr (peace be upon him) used the plural "we" in some instances (so we intended) due to the great gifts and talents Allah bestowed upon him, such as the knowledge with which Allah specifically endowed him. This is a form of proclaiming Allah's bounty. In other instances, he used the singular pronoun (so I intended) out of humility, being an individual among human beings, and without considering the privileges with which Allah distinguished him.