You're right, but this example shows that Hungarian is a bit more flexible in this respect.

Bare nouns, that is nouns without a definite or an indefinite determiner, are often used in the singular in Hungarian when they are translated into English in the plural:

Virágot vettem. — ‘I bought (some) flowers.’

So when we're not talking about a specific group of children, it's fine to say Nem látok gyereket and Nem látok gyerekeket to mean the same things. When we're talking about a specific group, you'd obviously say a gyerekeket, in the plural!

Both I don't see children. and I don't see any children. can be translated as Nem látok gyereket.. It's hard to pin down the difference between these two English sentences, I think, but both are captured by the Hungarian.

I think it could go either way.

Kids = kölykök, kid = kölyök. The "kölyök" is synonym "gyermek" or "gyerek". "I do not see a kid" also a good translation. The Hungarian says "Nem látok egy gyereket sem." The other traslate "kid" = srác, fiú, gyerek.