Are they currently doing Urgent Travel Service or only Life or Death emergencies?

Yes. But you have to call to make an appointment no matter the issue. I had an appointment set for the same day I had a flight to the bahamas. I had all my documents in hand and an appointment (which must be done by phone). Everything was processed and my passport was given to me around noon. If you don't have an appointment, the security guard will NOT let you in no matter what.

You have to have proof of international travel within two weeks but not reason for travel required.

They are doing both. You will need an appointment and travel verification at booking.

To add to what Napoleon said, if you can’t get an appointment just email your government officials, that’s how I got my appointment.