As defined by the IRS: 

“An enrolled agent is a person who has earned the privilege of representing taxpayers before the Internal Revenue Service by either passing a three-part comprehensive IRS test covering individual and business tax returns, or through experience as a former IRS employee. Enrolled agent status is the highest credential the IRS awards. Individuals who obtain this elite status must adhere to ethical standards and complete 72 hours of continuing education courses every three years.

Enrolled agents, like attorneys and certified public accountants (CPAs), have unlimited practice rights. This means they are unrestricted as to which taxpayers they can represent, what types of tax matters they can handle, and which IRS offices they can represent clients before.“

US citizens have IRS filing obligations no matter where they reside in the world. The requirement to file will depend on your individual situation, but for most people you will find that you do need to file a federal tax return every year.

The word “resident” is often confusing in this question. If you are asked this by a foreign financial institution, what they are likely asking is if you are obligated for federal tax filing. If you are a US citizen or “green card holder” (US Lawful Permanent Resident) or physically resident in the US you will always be resident for federal tax purposes.

In most situations you will find that you do need to file a tax return, as holding lawful permanent resident status in the USA obligates you to IRS filing requirements until you formally relinquish your green card status. Even if your actual green card has expired, until you file the required documentation with the IRS your filing obligations remain.

Before replying to any letter from a tax authority it is important that you get the advice of a professional tax advisor.

Most foreign financial institutions are sharing various details about their US taxpayer clients with domestic bodies - who then share this information with the IRS/Treasury department.

The Foreign Account Tax Compliance Act (part of the HIRE act) is the law passed by the US legislature that compels foreign financial institutions to report on foreign assets held by their US account holders - which will otherwise be subject to withholding requirements. 

FBAR is another name for the FinCEN Form 114 and was formerly known as the Report of Foreign Bank and Financial Accounts. It is a required form for any US Federal tax payer who meets the filing threshold - the threshold being quite low as it was set in the 1970s.

This form was introduced by FATCA and requires much of the same information as the FBAR - with some notable exceptions and additions. The filing requirement is variable and in general has a higher threshold than the FBAR requirements.

The substantial presence test is a test to determine whether a non-US person is a tax resident for federal tax purposes.

This is a treaty between the US Federal tax system and the UK that is designed to prevent double taxation between the two countries.

In countries where there are double tax conventions, most situations are covered to prevent double tax. Where there is no double tax convention, then US domestic law may make provision to avoid double tax.