Ritcher got possessed because he canonically got the bad ending in Rondo
- In the Flashback battle at the beginning, Ritcher only fights forms 1&2 of Dracula, not his true form
- The true form is only fought in the good ending of Rondo of Blood which requires defeating Shaft's Ghost
- Thus, because Shaft's Ghost is still out there, he was able to possess Ritcher.
Alucard can't, or doesn't bother to, distinguish between the Belmont descendants.
It's been ~300 years since Castlevania III and yet when told a "Belmont" is storming his father's castle, the first person who comes to mind for him is Trevor. He also refers to Richter as "son of Belmont", as if sons of Belmont were bog-standard (well, there's a whole village of them in Ecclesia but that's still a very tiny slice of humanity). It's not until Julius that there's a descendant worth being on first name basis with.