This can be visualized nicely by an example:
Let’s say there are two islands in the world. And let’s just say island A only produces apples and island B only produces bananas. Also, the (real) exchange rate is one apple for one banana.
Now, for whatever reason, island A exports 20 apples but imports 30 bananas (a trade deficit). It now owes goods of the value of 10 apples/bananas to island B. How can it serve this debt? (If it were to send goods to the other island, its exports would rise by definition, and the trade deficit would disappear.) Instead, island A makes a promise to pay back the debt in a later period to island B (foreign debt). Instead of debt contracts, island B can also trade the excess bananas for shares in the production of A of the same value, which is equivalent.
Regarding question 2: A domestic loan has by definition a borrower and a lender on the same island. This always nets out to zero debt when aggregated to the island level. Hence, it can’t change the island’s debt position vis-à-vis another island.
Regarding question 3: Note that so far, we haven’t even mentioned money. The trade effects can be entirely explained by real variables. If we introduce currencies on both islands, there must be a foreign exchange market. This market for currency only clears if the exchanged currencies are of equal value (in real terms). It does not matter if you pay in the producer’s or the buyer’s currency, the currency for buying 30 bananas is always of higher real value than the currency to buy 20 apples. Demand and supply of currency won’t cancel out, so the foreign exchange market does not help you to settle the debt.