Many adjectives and adverbs can be modified by the adverb "very", so it is a bit confusing.
"Slow" is an adjective and "slowly" is its corresponding adverb. Adjectives typically modify nouns, but not verbs, and adverbs modify verbs and some other words, so "slowly" and "badly" are correct in your examples because they are modifying the verbs "drives" and "built".
You will sometimes hear people say *"He drives slow", and although it has the same meaning as "slowly", it is grammatically incorrect.