Question

Which sentence uses correct punctuation and capitalization within parentheses?

Answer 1

The right senteces is "Beginning in the seventeenth century, the rulers of Japan (why did they do this?) had forbidden contact with foreigners." because usually punctuation and capitalization are left ouside of the parenthesis, expect when it is after a ? or a dot. 
In this case the period inside the parenthesis is simple and it has a question mark, so it goes without capitalization at the beginning and the question mark is right before the conclusion of the parenthesis. 

Answer 2

Beginning in the seventeenth century, the rulers of Japan (Why did they do this?) had forbidden contact with foreigners.