The $350 billion from question 1, and the 'it' from question 2, both describe the 'current account deficit'. The word 'deficit' means the difference between how much money is coming in, and how much is going out.
So in 2002, the government spent $350 billion more than it earned. It (the deficit) has doubled since then, so in a given recent year the government spent $700 billion more than it earned. And yes, for Q.3, 'the U.S. is a net (net = total) debtor ...', means the U.S. owes the world approximately $3 trillion in total.
Essentially, deficit is the amount of new debt created in a given year. The net debt is the total of all the debt built up over past years.