We do not currently know of any adverbs for comprise. Using available adjectives, one could potentially construct nonstandard adverbs such as comprisingly, comprisedly, comprizingly or comprizedly.

Is comprising grammatically correct?

The correct version put forward by grammar guides is to use "composed of" or "comprises" such as "the cake is composed of flour and eggs" or "comprises flour and eggs." Beginning in the early 20th century, a number of usage guides decided that there was something wrong with the way that some writers used comprise.

Is correctly is an adverb?

In a correct manner.