Is it permissible to supplicate for the alteration of a physical defect that emerged after birth, or is submission to divine decree obligatory? And is supplication alone sufficient, or must one pursue treatment along with supplication?

It is permissible to supplicate for healing and for the facilitation of treatment. This does not contradict submission to divine decree, for supplication itself is part of divine decree and is commanded by the Sharia. Just as the Muslim is commanded to seek treatment, for Allah has not sent down a disease except that He has sent down a remedy for it.