Hi, and welcome to the forum.

As an American, you are subject to US income taxes wherever you live in the world. As an overseas resident, you are eligible for the Overseas Earned Income Exclusion - which is something in the area of $87,000 (it changes year to year) you can exclude from your income each year (using form 2555 - you still have to report your worldwide income). Anything above that you apply Foreign Tax Credits, but since there is no income tax in Dubai (or so I hear), you have no tax to credit against your US tax liability, so you actually pay taxes on it.

Social security depends on your situation. If you are working for a US employer and the employer withholds it for you, there is nothing further to do. (In the case of a temporary assignment overseas, some employers will continue to withhold US SS in order to keep you in the system while you are overseas.) If your employer doesn't do this, you just lose those years in the US SS system.

For details, see IRS Publication 54.
Cheers,
Bev