Learn Finnish: Nukuitko kunnolla? - Did you sleep properly?

The word kunnolla is actually the adessive case (the -lla ending) of the noun kunto, which means "condition" or "fitness". While it literally means something like "with condition", it operates as a standard adverb of manner meaning "properly", "thoroughly", or "soundly".

Could I just use hyvin instead of kunnolla here?

Yes, Nukuitko hyvin? is perfectly natural and simply means "Did you sleep well?". Using kunnolla adds a slight B2-level nuance of sleeping "properly" or "thoroughly", emphasizing that you got a sufficient and restorative amount of rest.

Why does nukuitko have a weak consonant grade (one k) when the infinitive nukkua has two?

Consonant gradation depends on whether the syllable is open or closed. The second-person singular ending -t closes the syllable (nu-kuit), triggering the weak grade (k). The question enclitic -ko is added afterward and doesn't change this underlying conjugation. If it were third-person, the syllable would be open and remain strong (nukkui).