You aren't tax exempt. The Foreign Earned Income Exclusion (FEIE) applies ONLY to earned income and it only applies to the first $103,900 of earned income. To qualify, one must actually live and work in a foreign country. The tax rate on non-excluded income is higher because the calculation includes (temporarily) the excluded income.
Second, what Social Security? To qualify for Social Security benefits, you need to have paid into the system. If you are living in another country and working for an employer, chances are you aren't paying into the US system. There are a number of countries that have a Totalization Agreement with the US that will increase the odds that you are eligible for something. If you have been out of the US for only a few years, this may or may not impact the benefits you receive. If you have less than 35 years of covered earnings *or* all of your high income years were in other countries (or both), you may be in for a surprise. This article states the Windfall Elimination Program can further reduce your benefit. Ditto working more than 45 hours a month.
From 62 to full retirement age, there is that earned income test that reduces your benefit for every $2 you make over $17,640. There is also a test that can include the money you do get into income at up to 85%. That will then, in turn be taxed at a higher rate than you'd think due to the FEIE.