Your first question is fairly formal, and you could reply equally formally 'I attend St Paul's [school]'. However, since 'attend' means 'to go to', your first answer would be fine 'I go to St Paul's [school]'. Notice that I've used 'St Paul's' as it's usual to use an apostrophe to indicate that this is the school of St Paul, and most people would not bother to add the word 'school' ... 'I go to St Paul's' or just 'St Paul's' (although, you need to check that short answers are acceptable).
As a British English speaker, I would not use your second question, preferring 'Where do you study?' or 'Where are you studying?', and then the answer could be 'I'm studying at St Paul's [school]' or 'I'm at St Paul's [school] ' or 'St Paul's [school]'.
Hope that helps