Learn Icelandic: Blásturinn klárar hann miklu hraðar núna. - The blowing, he finishes much faster now.

This is called topicalization. By putting the direct object (Blásturinn) first, the speaker puts special focus or contrast on it, as if saying 'As for the blow-drying...'. Because Icelandic strictly requires the verb to be the second element (the V2 rule), starting with the object forces the subject (hann) to swap places with the verb (klárar).

Since Blásturinn is the direct object of klára, shouldn't it change its form to be in the accusative case?

It actually is in the accusative case! For a specific group of masculine nouns ending in -stur, such as blástur, lestur (reading), and rekstur (operation), the nominative and accusative forms are completely identical.

Why do we use miklu here instead of mikið or mjög?

When modifying a comparative word like hraðar (faster) to mean 'much faster', Icelandic uses the dative form, which is miklu (literally 'by much'). You will see this dative pattern used with almost all comparatives, such as miklu betri (much better) or miklu meira (much more).

Is hraðar the comparative form of an adjective or an adverb here?