an HP question that isn't about ship wars! ([boggle]!)

so Seamus Finnigan is a halfblood, right?  dad's a muggle, mam's a witch, nasty jar for father.  ditto Tom Riddle, yeah?  his mother was a witch and his father was a muggle, which has been clear since ... gosh, for a long time, at least since Goblet of Fire if not as far back as Chamber of Secrets.

actually i suppose i have two questions -- (1), do we know of any cases of a halfblood whose mother is a muggle and whose father is a wizard?  and don't say ( spoiler )

, because my whole point about that -- and about Harry as well, incidentally -- is that Lily Evans Potter (and ( spoiler )

) was a witch, albeit a muggle-born one.  so (2) where is the line drawn?  Harry is the child of a witch and a wizard; why is he not considered pureblooded?  or, if he's a halfblood, surely he must be a different sort of halfblood than Seamus Finnigan, one of whose parents is an actual honest-to-god muggle.

and actually, (2a) what if one parent were a squib?

[eta:  okay, so i'm high -- actually ( spoiler )

.  but the question remains about harry and halfbloodedness, though blah blah grandparents, nuremberg, see comments.  [g]]