https://www.pa.ng.mil/Community/Mailing-Deployed-Service-Members/

Basically their unit (or ship) gets assigned a special military PO box and the military takes care of it from there. USPS says you just pay like a domestic letter or package. It's almost certainly subsidized by the military. I assume the other package carriers are similar.

Should be able to send to the service member's unit at FPO or APO depending on if they're in the army, navy, etc. This page https://www.usps.com/ship/apo-fpo-dpo.htm has more info.

You can absolutely receive mail and packages when deployed in the military, even during wartime. When I was in the USMC, getting mail while out in the field was a bit of a psychological life line.

It's actually kind of neat. They have their own "state" codes for the Air Force or Navy, and that's how the mail is handed over to the military. They do have to give an apo or the like, but the deployed know that before leaving so family knows how to write.

It gets murkier once it's inside how they route the mail, don't know for sure, but as long as you follow USPS guidelines it'll get to them. So, part of your answer at least

https://pe.usps.com/text/pub28/28c2_010.htm

They had their letters delivered to them at their duty station APO before their mission deployment. There's no fucking way they could get a letter from home in the middle of combat during Operation Overlord.

I'm sure you imagine a Skyrim courier interrupting a U.S. soldier brutally wrestling and slitting a Nazi throat to tell him your grandmother said hi with included slutty nude photo in a Western Union telegram.

For WWII specifically, anything written might not actually be sent. V-Mail services photographed letters, reduced them onto microfilm, and reprinted them overseas. A lot of people were sending a lot of mail and paper is fucking heavy.

AFAIK, addressing worked about the same way it works now: you're given an address for a specific person, at a somewhat-abstract location. Sometimes it's a very concrete place - no pun intended - like a permanent airbase or an actual city. Sometimes it's a boat. Sometimes it's a "forward operating base," which falls somewhere between no-fun-allowed paintball facility and Burning Man with more grabassing.

Overseas military addresses must contain the APO or FPO designation along with a two–character “state” abbreviation of AE, AP, or AA and the ZIP Code or ZIP+4 Code.

AE is used for armed forces in Europe, the Middle East, Africa, and Canada; AP is for the Pacific; and AA is the Americas excluding Canada.

Also:

APO / DPO / FPO basics

APO – Army/Air Force Post Office. The Military Post Office for Army and Air Force personnel
FPO – Fleet Post Office. The Military Post Office for Navy and Marine personnel
DPO – Diplomatic Post Office. The preferred designation for mail addressed to Department of State overseas post offices.
MOM – Military Ordinary Mail. Mail originating from the Department of Defense.
MPO – Military Post Office. Provides postal services for military personnel.
PAL – Parcel Air Lift. An expedited service for Package Services is available for an additional fee.

Anyway you can also send "unit boxes" for a whole group, but I think you're still supposed to address them a specific individual.

To send a piece of mail to a ship, you send it to a Fleet Post Office, listed as the city and state.

For example, if the ship is stationed in the pacific fleet (AP- armed forces pacific), you’d send it to:

Jane Q Sailor USS Whatever FPO AP (the unit zip code)

And the mail would be forwarded to the ship anywhere in the world to meet the ship with supplies. I don’t know all the codes, but they’re all similarly formatted.