Is it permissible for seven people to share in the sacrifice of a calf, with the father's share being a charity, and will it be counted as a sacrifice for everyone?

The minimum permissible share in a cow (for sacrifice) is one-seventh. If the sacrificer's share is one-seventh, then his share is sufficient and valid. It is not a condition that all participants intend to offer a sacrifice. So, if one of them participates with the intention of eating the meat, or giving it as charity, or with less than a seventh, this does not harm the one who intended to offer a sacrifice.