The area map is the overland travel map. It looks like a road map.
The PC plus up to three other characters can travel. The PC must always be part of the traveling party.
Characters with higher levels of the Survival skill will be able to spot wild sources of food on the area map. If you know where they are, you can travel to them, harvest the food (automatic, not pick everything up manually), and come back if they pop up again.
Random encounters don't stay on the map, but actual locations are marked. You should have some indication on there to tell you if you've visited and possibly when you last visited the location.
You can stay out into the night, but you can only rest at the school, so you will have to return there eventually.
The groups travel is based on the player's skill plus a bonus derived from the survival skill of the allies.
Loot is location specific. Supermarkets have more food, hospitals more medicine, etc… Loot is finite. The only reason to go back to a location is if you didn't get everything the first time.
It’s possible that a location could have fewer resources over time or the small chance that something else could have happened to clean out the area entirely. There are always urgent reasons to do almost everything in the game - that's part of the decision making process.