When working with children, it is important to understand the activities that help to settle them and those that help to stir them or activate them. Generally, when you ask children to copy, to colour or to listen to a story, they settle down and are quiet. Games involving moving and competition generally stir them. All children are different and they are stimulated or subdued by different activities. I suggest you try different exercises with the class and observe the effect these exercises have on your students. When you understand this, you will have a very useful tool.
With your 6-8 class, you’ll be able to start classes with an activity that calms them down and when you think they are too quiet and need livening up a bit, you’ll be able to introduce an activity that will stir them into action. You’ll be the person who decides what the atmosphere is.
I also suggest that you have a short talk with the class. You’ll need to do this in their own language. If you don’t speak Korean, I suggest you ask somebody to explain to the children. I’m guessing that they ask for bingo, stickers and presents because they received these with their teacher last year. Explain to them that bingo, stickers and presents are nice and enjoyable and that they will continue having certain treats this year. Also tell them that they are a year older and as such you prefer to use these items as rewards for when they work well. Tell them they will still receive treats (games, stickers or whatever you choose) but that they will have to show you that they have worked hard before receiving these treats. For example, they’ll still play bingo but not so often. On the other hand, they’ll learn to play other games that they will enjoy just as much. Remember that children learn through playing, so you will need to include games but that you are the person who decides when they play. If you decide to give rewards when they work hard, you will need to stick to whatever you say. Don’t give rewards if they haven’t worked well.
Incidentally, I forgot to say yesterday that I can see why you think there is no point in teaching English to the 4-5 age group. It can be frustrating at times but in fact children of that age do learn a lot. They learn by just listening and being in an English environment. They are also seeing that studying English is a positive experience which will help motivate them in their later studies.
I hope this will help you. Please write in again if you would like more ideas.