"Did he use the spoon successfully?"
Translation:Používal tu lžíci úspěšně?
FWIW, I'm native AmE and see some difference in meaning between the use of the two adverbs. I would say that the use of "successfully" here suggests that he accomplished his (or someone's) purpose in using the spoon. On other hand, the use of "correctly" suggests that he used the spoon in the way that a spoon is intended to be used.