Yaḥliqu is a Form I imperfect verb from ḥ-l-q, meaning 'to shave.' Yuqassiru is a Form II imperfect verb from q-ṣ-r and here means 'to shorten.'
Aw presents the permitted alternatives. In al-ḥalqu afḍalu, al-ḥalqu is the nominative subject and afḍalu its predicate, making a preference between two available methods.