Shakya were oligarchies republic was vessels state of Kosala before the birth of Budha(Sidharth), and in 5 BCE Kosala king Virudhaka, son of Pasenadi and Vāsavakhattiyā, the servant of a Shakyan chief named Mahānāma, ascended the throne of Kosala after overthrowing his father. As an act of vengeance for perceived slights against his mother, a servant before her royal marriage, he invaded the Shakya territory, massacred them and annexed it. so there was no claimant of Shakya throne.
Sidharth(Budha) son Rahula had become pupils of Budha. so there is no question of GOD hair.
for becoming India Buddhism - Harsh Vardhan had a son to propagate his line . then you will have a capable North India empire which can fight Mulsim conquest and keep their grip on south India successfully. you have know that North Indian resisted Muslim conquest for 500 years .