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Suppose you were talking to your friend, in a casual conversation. Friend: Was that your father whom we saw yesterday at the school? You: Yes, that was my father.
I'm quite confused whether to use "that is my father" or "that was my father".
I feel it should be "that is my father", because the question establishes the fact that my father was seen in the school yesterday and be it today, tomorrow, a week or a month later, he's still going to he my father.
Both are possible. In the context you give "was" is probably more likely to be used. The question has established a past tense, and we are talking about a past event (the visit of a person to school yesterday).
Your question and answer are very far from "casual conversation" in style. They are highly formal. Don't use "whom" or "father" in casual conversation.
Was that your dad we saw at school yesterday?
Yeah, that was him.
The question is, "Was that your father?", so the answer is, "Yes that was my father." Or, of course, it could be, "No, that wasn't my father."
Here is a present-tense example.
Is that your father standing over there? Yes that is my father.
