Yes, you should file your FBAR, even if it's late or delinquent. As of now, there's no monetary penalty, if you meet certain qualifications (see below).
Yes, amend your return first to properly report all income. File your FBAR as soon as possible to get in compliance.
This, from the IRS' Report of Foreign Bank and Financial Accounts:
Delinquent FBAR Submission Procedures
Taxpayers who have not filed a required FBAR and are not under a civil examination or a criminal investigation by the IRS, and have not already been contacted by the IRS about a delinquent FBAR, should file any delinquent FBARs according to the
FBAR instructions
and include a statement explaining why the filing is late. All FBARs are required to be filed electronically through FinCEN’s
BSA E-Filing System
. Select a reason for filing late on the cover page of the electronic form or enter a customized explanation using the ‘Other’ option. If unable to file electronically you may contact FinCEN’s Regulatory Helpline at 800-949-2732 or 703-905-3975 (if calling from outside the United States) to determine acceptable alternatives to electronic filing.
The IRS will not impose a penalty for the failure to file the delinquent FBARs if income from the foreign financial accounts reported on the delinquent FBARs is properly reported and taxes are paid on your U.S. tax return, and you have not previously been contacted regarding an income tax examination or a request for delinquent returns for the years for which the delinquent FBARs are submitted.
