Past tense or present tense?

Hi everyone, I got a few questions here regarding the usage of past tense and present tense.

Q.1: "A great mathematician found out that ..... He also discovered that... Who is he?"

For the sentence above, should we use "Who is he?" or "Who was he?", since the first few sentences are in the past tense forms.

Q.2: A comprehension is given in past tense form. In one of the questions, it asks "Why was John unhappy?"

To answer this question, should we write "It is because his cat had died." or "It was because his cat had died." It seems that the word "is" after "it" is not connected to the explanation, so I think the word "is" should be used?

Thanks for the reply. Another one: "Fermat’s Last Theorem remains unsolved for centuries until it was proven in the year 1994. "

Can we combine both present tense and past tense in 1 sentence? And should we write "...until it is proven..." or "until it was proven..."?