I think the difference is that in English the adverb is negated white in Czech the verb is. Už nespím = Already, I am not sleeping - means that the not sleeping is happening already. So I might have been sleeping, but now or sometime before now I stopped. I am not yet sleeping means that the sleeping is not yet happening.
Sometimes can be one word, yes https://dictionary.cambridge.org/grammar/british-grammar/any-more-or-anymore