If a player surrenders and all other players accept their surrender, what happens to their territories? I assume they go neutral, but do the neutral territories end up with any armies? For reference, the game started with 3 armies on every territory. 

When a territory goes neutral because of a surrender or a boot it keeps the amount of troops the player had on it.

I assume the same thing happens if someone gets booted.

Correct, a booted player's territories become neutral with the same number of armies on them.