No, Moriarty only appears in the final problem. There are times when Holmes and Watson talk about or mention him in the later cases.
Irene Adler was mentioned in other cases, but didn't appear. But just in passing.
I don't think they said he always wears black.. and he's considered Holmes's rival 'cause he's always ahead a step or two. But Holmes outwitted him in the end.
Jack the Ripper? Not that I remember.