Both are/were writers
 

Bertrand russell was a writer.

Nicolas Coleridge is a writer.

Both are/were writers.

In the 3rd sentence, could you tell me what tense should be used?

Re: Both are/were writers
 

Neither. As Russell is dead and Coleridge is alive, neither verb is appropriate for both writers. So you'd have to change the sentence to eg BR was a writer and so is NC./ BR was a writer, as is NC.

Re: Both are/were writers
 

Marvellous.

Thank you very much indeed.

I never thought of such a change.