I want to address a few small errors in the sentences first, just because they're tiny things that could make a big difference.
The phrase 'problem children' isn't one I've heard before. I don't know what you mean here, but it might be better to say something like 'challenged children' or 'misbehaving children'.
When you talk about other students in the plural, say 'others' instead of 'other'.
Now, for the question:
Misbehaving children not only interrupt their classes, but also prevent themselves and others from learning.
The sentence above is correct, natural and formal.
Misbehaving children not only interrupt their classes, but also they prevent themselves and other from learning.
This sentence is more natural if you swap 'also' and 'they' around in the second clause. Adding in the 'they' is more informal, and would normally be omitted. I think this is what you're after when you look for which is 'official' and 'colloquial'. The first is more official and the second is more colloquial in this case.
When you add 'not only do' to the beginning, it becomes more natural to add in the 'they' in the second clause. This is because they haven't clearly been defined as the subject of the sentence due to the emphasis that they cause several problems. It is definitely better to say:
Not only do 'Problem' children interrupt their classes, but they also prevent themselves and other*s* from learning.
(Note the swap of 'they' and 'also' and the plural 'others'.)