U.S. retirement benefits normally need 40 quarters (10 years) of credits. If you split a career between the U.S. and South Korea, you might fall short in each country alone. As long as you have at least 6 quarters of U.S. credits, the agreement lets you add your South Korea credits to reach eligibility — the U.S. then pays a benefit pro-rated to your U.S. credits only.
A Certificate of Coverage is the document that proves you're exempt from one country's social security. For U.S. coverage, the employer requests it from the SSA Office of Earnings & International Operations. South Korea's authority issues the equivalent when South Korea covers you.
Under the U.S.–South Korea agreement, a worker sent by a U.S. employer for 5 years or less normally stays under U.S. Social Security only and is exempt from South Korea's system. Your employer obtains a U.S. Certificate of Coverage as proof. Beyond 5 years, coverage shifts to South Korea.
Yes. If you have at least 6 quarters (about 1.5 years) of U.S. credits, the agreement lets you combine ("totalize") your U.S. and South Korea credits to reach the 40-quarter (10-year) threshold for a pro-rated U.S. retirement benefit.
The agreement has been in force since 2001.
Pension taxation depends on South Korea's domestic law and the separate U.S.–South Korea income tax treaty (if any), not the totalization agreement. The totalization agreement only governs which country's social security system covers you and how credits combine. Confirm pension taxation with a cross-border tax advisor.