"Every kid here has a pencil."
Translation:Mọi đứa trẻ ở đây đều có bút chì.
You should read this thread on DL.
""Đều" works as an Adjunct to indicate there is something similar between them."
Actually, I'm not sure đều would work well with action verbs. So far I encountered đều in sentences stressing people have a quality in common, not actions. (see also this question)
You are having trouble with this kind of sentence because in English there's no difference between having uncountable pencil and having specifically one.
If I used the Spanish grammar in English I could say:
"I have a pencil" (specifically, one and only one pencil)
"I have pencil" (usually is one, but I could have more, the important here is not how many pencils I have, the important thing is that I don't need a pencil and I can write).
Vietnamese seems to have the same mechanism, so to understand those sentences you need to think if it is one specific thing or is more undetermined.
I think for English speakers must be hard because you don't do this distinction in your language. The good news is that I think if you use "một"+classifier is still kind of correct, and I'm sure you will be understood.