Is it obligatory for one who is observing a voluntary fast to refuse his friend's invitation to eat, or to accept the invitation and break his fast?

It is permissible to accept your friend's invitation and drink tea with him, especially if it brings him comfort. A person observing a voluntary fast is master of his own will; he may fast if he wishes, or break his fast if he wishes. It is permissible for you not to break your fast, as the Prophet, peace and blessings be upon him, said: "If any of you is invited to a meal, let him accept. If he is not fasting, let him eat. If he is fasting, let him supplicate." If the fast is obligatory, then eating is not permissible. If it is supererogatory (nafl), then breaking it or continuing it is permissible. It is better to break the fast if your fasting would cause hardship to the host of the meal; otherwise, it is better to complete the fast.