Could my brother's death have been caused by the evil eye? Can the evil eye be removed by ruqyah and supplication? Is it wrong to admire others while mentioning God? And how does one know if their own eye inflicts harm?

Your feeling of guilt over your brother's death due to your admiration for him is unfounded. Not every admirer is an envier, especially since you consistently say, "Masha'Allah, Tabarakallah (What Allah wills, blessed be Allah)." If your brother was exceptional, you should not accuse yourself alone. As for the healing of the afflicted by the prayer of the envier, it is not necessary. The prophetic remedy for preventing the evil eye is to pray for blessings, and for its treatment, the envier should perform ghusl (definition) (ritual bath) or wudu (ablution). Praising someone in front of people is permissible, but one should limit it to those who wish them well and pray for their blessings, because every possessor of a blessing is envied.