What is our duty towards our brother who passed away at eight months of age, and whom our father buried without washing, praying over him, or performing an 'aqiqah, given that our father was unlearned and we were young and unaware of the rulings of Islamic law?

Your father erred by not washing your brother, and his ignorance is no excuse. Since time has passed, do not exhume the grave or demand his removal. As for praying over him, some scholars have issued a fatwa permitting it, and that death does not invalidate his 'aqiqah. Therefore, pray over your brother's grave, and it is recommended that your father perform the 'aqiqah for him now.