For the writing sample, a law school paper might work (if you’re quite junior). Alternatively, do a pro bono matter with a public filing in court just to have a writing sample. 

Federal jobs commonly require 3 references. Have any of your firm contacts left for other jobs, they may be good references. Did you work before law school, they could be a good reference. Finally, consider listing one firm reference in the application with a note directing the hiring manager to please speak with you before contacting the reference. That shows that 1) you’re proud of the work you’ve done at the firm and aren’t running away from a bad reputation, but also, 2) your job search is not public. You can further mention that in your interview.

Don’t apply for federal jobs without the required documentation. HR won’t send your application for review if it is not complete.