I’ll start by answering your question about EFL and ESL. ESL stands for English as a second language. This refers to, for example, people living in India who use English regularly but English is not their mother tongue. It’s similar to the use of French in countries such as Lebanon and Morocco. In these countries Arabic is the mother tongue and French is the second language. EFL stands for English as a foreign language and refers to situations such as Spanish people in Spain learning English. Here, English really is a foreign language. I don’t know which country you live in so I’m not sure whether you should teach EFL or ESL. In any case, with young children, I don’t think there would be a major difference between the two approaches.
As for skills work, I think you should focus on listening and speaking as much as possible with the younger children (6-8 years old). They are probably learning to write in their mother tongue and it can be very confusing to write in a foreign language and can affect their abilities in their mother tongue. At this age, keep writing to a minimum, e.g. copying vocabulary. The older children should be able to write more extensively; they should be able to produce a paragraph of writing, unless they are absolute beginners. Nevertheless, you should try to do as much listening and speaking as possible and keep writing exercises for homework.
When teaching children, you need to introduce a lot of variety. You will need to change activities often. Smaller children are happy to repeat activities, for example a favourite game or song can be repeated. Older children will appreciate something new and can concentrate for longer periods of time.
The above are very general comments about teaching children. Please feel free to write in again if you would like to know about specific situations.