1. If the external sector is in deficit overall and GDP growth rate is faster than the real interest rate, then:

Neither the private domestic sector or the government sector overall can pay down their debt liabilities.
Either the private domestic sector or the government sector overall can pay down their debt liabilities.
Both the private domestic sector and the government sector overall can pay down their respective debt liabilities.

2. The debt of a government which issues its own currency and floats it in international markets is not really a liability because the government can just continuously roll it over without ever having to pay it back. This is different to a household, the user of the currency, which not only has to service its debt but also has to repay them at the due date.

3. The fact that inflationary pressures have followed large scale quantitative easing programs conducted by central banks validates the mainstream Quantity Theory of Money, which claims that growth in the stock of money will be inflationary.