When using ice to keep foods cold, the food container must be surrounded by ice to the level of the food. which is the best way to tell if the food is staying cold enough?

You should use a thermometer. 

If you want to keep food cold in ice water
put the food in a plastic bag zip it up put the bag into another zip lock bag
put the ice/ice water in the big plastic bag. or just use the special bags which keeps your food still fresh and cool.