I am so sorry once more to read about your ordeal. That is quite outrageous and at the same time incredible.
Question 1: Do you think that a court would consider the employer's actions to be outrageous?
Response 1: Yes, based on the information that you have provided.
Let me say that I have never been arrested or have ever had any interaction with the police. Question 2: Can I sue the responsible persons individually for intentional infliction of emotional distress?
Response 2: You need to sue the agency and the individuals. The agency is vicariously liable for the action of its employees.
Question 3: How do I effect service of process on these individuals who are federal employees? I don't know where they live because their home addresses are not a matter of public record. Is there a certain Federal entity that is served?
Response 3: You would have to use the address where they work and have a process server serve them at work in accordance with Federal Rules of Civil Procedure Rule 4 (e) and (i). Service on the agency must be made pursuant to Federal Rules of Civil Procedure Rule 4(i)
"(i) Serving the United States and Its Agencies, Corporations, Officers, or Employees.
(1) United States. To serve the United States, a party must:
(A)(i) deliver a copy of the summons and of the complaint to the United States attorney for the district where the action is brought—or to an assistant United States attorney or clerical employee whom the United States attorney designates in a writing filed with the court clerk—or
(ii) send a copy of each by registered or certified mail to the civil-process clerk at the United States attorney's office;
(B) send a copy of each by registered or certified mail to the Attorney General of the United States at Washington, D.C.; and
(C) if the action challenges an order of a nonparty agency or officer of the United States, send a copy of each by registered or certified mail to the agency or officer.
(2) Agency; Corporation; Officer or Employee Sued in an Official Capacity. To serve a United States agency or corporation, or a United States officer or employee sued only in an official capacity, a party must serve the United States and also send a copy of the summons and of the complaint by registered or certified mail to the agency, corporation, officer, or employee.
(3) Officer or Employee Sued Individually. To serve a United States officer or employee sued in an individual capacity for an act or omission occurring in connection with duties performed on the United States’ behalf (whether or not the officer or employee is also sued in an official capacity), a party must serve the United States and also serve the officer or employee under Rule 4(e), (f), or (g).
(4) Extending Time. The court must allow a party a reasonable time to cure its failure to:
(A) serve a person required to be served under Rule 4(i)(2), if the party has served either the United States attorney or the Attorney General of the United States; or
(B) serve the United States under Rule 4(i)(3), if the party has served the United States officer or employee.
Question 4: what is the statute of limitations?
Response 4: Two years from the date of the incident.
Question 5: is this tort governed by state or Federal law?
Response 5: State law.