If you block someone and play Hard Case to cancel the combat, is your
blocking vampire still tapped for succesfully blocking?
Card text. "untapped" "successfully performing"
> If you block someone and play Hard Case to cancel the combat, is your
> blocking vampire still tapped for succesfully blocking?
Yes. Successful block -> tap the blocker.
Does this then mean he has to be untapped from the beginning till the
resolution of the action?
No. Only when a minion is "successfully performing" the action.
An action is only successfully performed (or not) at resolution.