Who is my guardian in marriage under the aforementioned circumstances? Is it permissible for the ruler or the judge to be my guardian, or my female cousin’s son? What is meant by "al-ʿaṣabah" (agnatic relatives) and what is its evidence from the Qur’an and Sunnah?

The grandfather, who is the father of the father, is the guardian (wali) in marriage; otherwise, it is the paternal uncle. It is a condition that the guardian be a Muslim, and there is no guardianship for a non-Muslim, as Allah Almighty says: "And the believing men and believing women are allies of one another." It is not permissible for a more distant relative to be a guardian when a closer one exists, unless the closer relative refuses to marry off a suitable suitor, in which case the guardianship transfers, and his right is forfeited. The son of the maternal aunt and the maternal uncles are not guardians in marriage, because guardianship is specific to the 'Asabah (agnatic relatives), who are the male relatives from the father's side. The order of guardianship is: the father, then the grandfather, then the son, then the brother, then the nephew (brother's son), then the paternal uncle, then the paternal uncle's son.