We got our red card through the door too for my FLR! Good thing too as we're flying to Egypt on Sunday morning and REALLY needed those passports. Luckily the post office is just around the corner, I'm going to go at 7 when it opens because the hours are ridiculous.
As for ID to show them, they're pretty lax, I usually use a debit card, as long as it matches your name you'll be fine. Otherwise you need two letters or similar that have your maiden name.
We sent ours in on 22nd July for anyone else out there looking at waiting times. Our app is pretty straightforward. Caroline was born in Malaysia, but moved here at a young age, other than that there's nothing complicated about it.
Good luck to anyone else still waiting!