Am I obliged to slaughter a whole sheep, or is it sufficient to slaughter half of it, sharing it equally with my partner in the land after selling my share? And is it permissible to buy a small cow, dedicating half of it as gratitude to Allah and the other half to my family?

The conditional vow (nadhr al-tabarrur) must be fulfilled when the condition is met, and is not obligatory if the condition is not met. If the vow is conditional upon both partners selling their shares entirely, then it is not obligatory to fulfill it until the other partner sells his share, or it is permissible to fulfill it before the condition is met with the partner's permission. However, if each partner intended to make his vow conditional upon selling only his own share, then the one who sold his share must fulfill his vow without waiting for his partner. He should slaughter half a sheep as his vow, and it is permissible for him to slaughter a whole sheep or to share in half a cow.