hey mimi!
1 -- to me, it seems like that would be a not-so-good idea. as we've seen with muggleborn children whose parents have tried to prevent their enrollment in magical schooling, violent or negative magical outbursts tend to happen. i'd assume it would be pretty disastrous if an entire family tried to suppress their magical tendencies. so, while i'd say that yes, they could, i'd also say that it would not result in something that would be very constructive.
2 -- any "combination" of magical blood, other than muggleborns or purebloods, is considered halfblood. their "pure" blood would be a lesser percentage, but they'd still have magical blood and would still be considered halfbloods.
it kind of goes like this:
pure + pure(including squibs) = pureblood
pure + half = halfblood
pure + muggle = halfblood
pure + muggleborn = halfblood
and so on.
that said, muggleborns are said to have magical genes that show up at random, so i guess you could maybe work something out around that?
other than that, they'd just be halfbloods -- especially if they were aware of their magical heritage.

hope this helps!!
[ash]~ ashton[/ash]