Basic Idea:

Every nation has a comparative advantage in producing some goods, and a comparative disadvantage in producing other goods. It may be due to a relative abundancy of capital, labor, or other natural resources; specific types of resources (e.g., skilled vs. unskilled); or differing productivities. Specialization allows for more efficiency, creating mutually-beneficial gains from trade. These gains from trade are a significant factor in improving world-wide growth, and countries which specialize and exchange with others tend to grow faster.

South Korea: 50 million workers, 1 worker can produce 1 unit of hardware per week or 0.5 units of software.
U.S.: 150 million workers, 1 worker can produce 2 units of hardware or 3 units of software.
PPF: SK 50 m. hardware or 25 m. software, OC for software is 2.
US 300 m. hardware or 450 m. software, OC for software is 2/3.

Suppose that in autarky: SK produces 25 m. hardware and 12.5 m. software; US produces 150 m. hardware, 225 m. software; total is 175 m. hardware and 237.5 software.

In trade, SK produces 50 m. hardware and 0 software, US produces 130 m. hardware and 255 m. software, and total is 180 m. hardware and 255 m. software, more of both.

Average productivity differences.

Overall, countries gain, but some groups win and others lose. If we are relatively abundant in skilled labor and other countries are abundant in unskilled-labor, then we will likely specialize in and export skilled-labor products, and import goods which are produced with unskilled labor. This will lead to higher wages for skilled labor, higher prices for skilled-labor goods, lower wages for unskilled labor, and lower prices for unskilled-labor goods. Consumers of unskilled-labor goods benefit, but unskilled workers and even their employers may be worse off.

Governments use tariffs (import duties) or non-tariff barriers (quotas or other restrictions) to prevent trade. This favors specific import-substitutes, and discourages specialization according to comparative advantage.

Does protectionism work? In the short-run, protected groups benefit, and monopolies can be created. In the long-run, protected industries do not improve productivity as fast as those which must face international competition.

Countries trade goods and services, but they also trade their savings and investment - through savings in foreign banks, buying foreign stocks or bonds, or direct foreign investment in plant and equipment.

Balance of Payments = Current Account + Capital Account:

Current Account = Merchandise + Services + Income (exports - imports)

Capital Account = Net foreign savings (inflows - outflows)

Price of currency from foreign exchange market

Demand: imports, savings outflows

Supply: exports, foreign savings inflows

No. Decreased demand for imports would decrease demand for foreign currency, lowering its price (and making the domestic currency more expensive). Exports would fall too.

No. Suppose foreign workers started producing everything. Then we would be importing, but not exporting. Falling supply of foreign currency (who wants our currency if we don't have anything to sell??) would make foreign currency more expensive, and suddenly foreign wages would be high (foreign wage in dollars = foreign wage x exchange rate).

Between two countries, trade surpluses or deficits may result from multilateral trade. Suppose the U.S. exported food to Saudi Arabia, which exported oil to Japan, which exported cars to the U.S. The U.S. would have a surplus with Saudi Arabia and a deficit with Japan. Japan would have a surplus with the U.S. and a deficit with Saudi Arabia.

Overall, the primary cause is simply foreign savings inflows or outflows. We know: NX + Sf = 0 (Sf = inflows - outflows) and I = Sp+Sg+Sf. If I > Sp+Sg, then higher interest rates will attract foreign savings. More saving inflows will make foreign currency cheaper (and the dollar more expensive), causing exports to fall. Countries that save more than they invest have trade surpluses. Countries that save less have trade deficits.

Higher incomes usually cause imports to rise, but this must be accommodated by net savings inflows. Otherwise, foreign currency would just become more expensive (since we are demanding more of it to buy imports), and that in turn would encourage exports and slow imports.

Fixed exchange rates. Central banks offer to buy or sell foreign exchange with their domestic currency at a fixed price. If supply is greater than demand, the central bank must buy foreign exchange with new money. If demand is greater than supply, the central bank must buy its own currency back with its foreign exchange reserves, reducing its money supply.

Thus, a fixed exchange rate implicitly ties monetary policy to the balance of payments, and the resulting changes in the money supply will bring the foreign exchange market back into equilibrium.  An excess demand for the domestic currency, which is the same thing as an excess supply of foreign currency, will force the central bank to increase the money supply as it buys foreign exchange reserves, lower interest rates, and rising nominal incomes (either because of rising prices or rising real output).  Lower interest rates lead to reduced capital inflows and less foreign demand for the domestic currency.  Higher nominal incomes lead to more demand for imports, while rising prices make exports more expensive.

Similarly, an excess supply of the domestic currency, which is the same thing as an excess demand for foreign currency, will force the central bank to sell its foreign exchange reserves and reduce the money supply.  A central bank which is unwilling to let the money supply shrink (what Keynes called "the tail wagging the dog") may try to sterilize these effects by buying bonds in an open market operation.  The danger then, however, is that the balance of payments may remain in disequilibrium and the central bank will run out of foreign exchange reserves.  Once that happens, they must devalue their currency on the foreign exchange market; the results can be catastrophic because this injures those who hold domestic assets but need to buy foreign currency, and it undermines confidence in the central bank's reliability.
 

More or less.  Actually there are often four separate but related crises that happen:

1. A foreign exchange or balance of payments crisis, resulting from a fixed, overvalued exchange rate, and a central bank that sterilizes its foreign exchange transactions with open market operations.  It may be exacerbated by speculators who bet that the exchange rate is unsustainable, and by domestic and foreign savers who are worried about the real value of their assets.
2. A debt crisis brought about by foreign borrowing denominated in foreign currency.  When the domestic currency is devalued, this increases the domestic cost of foreign debt, puts further downward pressure on the exchange rate, and may make borrowers less solvent.
3. A speculative bubble in stocks, real estate, and other assets resulting from excessive optimism for continued rapid growth.  If this bubble bursts, this affects consumption through the wealth effect, makes some firms default on their bank loans, and by reducing lending also decreases investment.
4. A banking crisis from careless bank lending that results in an excessive default rate, making it harder for banks to lend and undermines confidence in the financial system.

Some countries, such as Thailand, South Korea, and Indonesia experienced all four of these.  Mexico experienced primarily #1 and #2, while Japan experienced #3 and #4 and Russia experienced #1, #2, and #4.