It isn't slang. It is informal, but not slang. If a phrase or word is slang, it means that it is restricted to certain group of people according to age ( e.g. teenagers) or ethnicity ( e.g. African Americans) or location ( e.g. a certain city or region) or another subgroup ( fishermen or gangsters, for example). The slang of these groups is not generally used outside these groups, and may well not be understood by outsiders. Everyone knows what 'kids' means, and everybody uses it. You wouldn't use it in every situation - it would be inappropriate in a legal document or business letter and you probably wouldn't used it in a formal essay, either. If that is what you mean by 'officially' , then yes, it should be avoided in some contexts. But it isn't slang. It is simply an informal word. If your teacher said it was slang, he or she doesn't fully understand what the term 'slang' means.

"Kids" is an informal word. It is not slang. English speakers, at least in America, use "kids" all the time. The word "children" is considered more formal, and it might be better for written English. So, in informal or day-to-day contexts, "kids" is absolutely fine. We use "children" in both spoken and written contexts that require a more formal word--such as on an application for a day care, or on any type of of government application. Also, some people might want to use children when they first meet. So they might ask, "Do you have any children?" But when the two people know each other better, then the use of "kids" would be natural and common. As in "Can you watch my/the kids for a moment while I clean out the car?"

I would consider it informal, so if I were writing a paper I wouldn't use it and would say "children" instead, but in everyday speech it's perfectly acceptable.

Yes, it is used for slang. But is also formal at times, it depends on who you are talking to. An older person is mostly exceptable, but around a boss you say children.

I think you can regard it as a slang word. Technically, "kid" is the desgination for a young goat. I do not know when people began referring to children as "kids" but though it may be slang, it is not an offensive generally. In the USA, we generally do refer to children as our "kids". For writing or academic work in school though, you probably should show a preference toward child or children. Have fun, kids!