Mars,
I think you are doing the right thing. Keep training the dog so it does not become possessive around food.
If you have good friends who can help you, I would suggest you get them to hold a piece of food to the puppy and say sit or stay and then give the puppy the food as a reward. Stay is a good one, as it teaches the dog to wait for the food, instead of grabbing it.
Let them touch the puppy, hold it, and if it is calm, another treat as a reward. Let the puppy meet as many new people, dogs and situations as you can, because when they are young, you can really socialise them well.
I have pulled my puppy's tail gently, and rewarded her for a calm response. I have picked her up when she is sleeping and caressed her, so she is easy-going about being disturbed when asleep.
And it is all so that when random children come to play with her, I have done what I can to make her comfortable in those interactions. She loves children and would be heartbroken if she didn't get to play.
And my little puppy (just a month older than yours) is great with children as well.
To me, it is part of my job as a responsible owner. But others who always leash their dog and never give it any freedom to engage with others, will tell you it is a terrible thing to do.