The culture of people eating lunch together was discussed. An extension of this is that eating alone is avoided because it is taken as a sign that a person has been excluded from a group or groups. To Koreans, being excluded from a group means there must be something wrong with that person and he should therefore be shunned by both those who know him and those who don't know him.
You should also avoid eating on the run because it gives the impression that you have been excluded if you are alone and is a sign that you are rejecting those that you are with if you eat by yourself when you are part of a group.
If are out and about by yourself and need to eat, go into a restaurant, even a fast food restaurant, to eat. Eating alone in public creates a bad impression - by eating in a restaurant, you reduce the stigma of eating alone. If you are with others then don't eat by yourself - suggest that the whole group grab something to eat and if they decline, wait until you get a chance to eat together or take your leave and find a restaurant or return to your accommodation to grab a bite to eat.
It is perfectly acceptable to drink a bottled non-alcoholic beverage alone in public. If you are with a group, it would be polite to ask the others whether they would like a drink and offer to pay for their drinks. It is not necessary to go to a restaurant for a drink - you can just purchase the drinks from a vending machine or convenience store. But buying yourself a drink without offering drinks to others would be considered bad form.
If you suffer from a medical condition such as diabetes that requires you to eat at irregular times, explain this to the group you are with and, if possible, carry and eat food which is fairly small and unobtrusive, such as candy or biscuits.