can i sacrifice vampire hexmage and NOT remove counters?

[Muk]

Can I sac a vampire hexmage without removing counters from anything?

[Arix]

Sure. Just target a permanent that has no counters on it (or even the Hexmage itself).

[hideseek]

can vampire hexmage sacrifice when tapped

[Kenji]

Yes. This is true of all creatures, really. You can sacrifice a creature whether it's tapped or untapped, as long as the card in question doesn't say otherwise. A creature also doesn't lose its abilities while it's tapped, although creatures that have to tap to activate their abilities obviously won't be able to tap while they're already tapped. =P

Fortunately, you don't have to worry, as very few spells/abilities actually require an untapped creature sacrifice. Betrothed of Fire is the only card that specifies that you need untapped creatures to sacrifice, as far as I can tell. If a card doesn't mention tapped or untapped orientation, you can assume (correctly) that the card doesn't care about the sacrificed permanent's orientation.