Why Do My Settlers Keep Getting Unassigned?

What does happen however is that when you accumulate too much puriefied water and food, settlers will no longer get assigned because there's no need to work the crops. In that case you'll need to empty the workshop of all water and food to be able to assign a settler to crops.

Do settlers automatically assign themselves?

Correct. New settlers will auto assign to food. Current settlers may need to be assigned to 1 food item, and it will auto fill the rest, when building a new area.

Do settlements with no settlers get attacked?

Without settlers you won't get any "defend the settlement" issues. But it can still get attacked while you are hanging out there. Red rocket has 1 to 2 raiders that can spawn nearby. They are really low level and so a few turrets placed around easily protect your settlement.