Additionally, what was the language spoken by the Egyptian population during the Islamic conquest of Egypt, and how were the invading arabs able to change the spoken language from the current language (I'm assuming Coptic) to Arabic?
The language of the ancient Egyptians was spoken in one form or another for over four thousand years, and continues to be used by the Coptic Church (similar to how the Catholic Church uses Latin). It is usually divided into six phases: Archaic Egyptian (3000-2650 BC), Old Egyptian (2650-2160 BC), Middle (spoken 2160-1300 BC, written 2160 BC-394 AD), Late Egyptian (1300-600 BC), Demotic (664 BC-450 AD), and Coptic (3rd-15th Century, still used liturgically). A major linguistic shift occurred between Middle and Late Egyptian, introducing grammatical gender, changing the word order, and moving from synthetic to analytic forms. Coptic Egyptian was slowly replaced by Egyptian Arabic over the centuries between the Arabic invasion and the 14th Century.
Hieroglyphics were used from the earliest writings until the closing of non-Christian temples in the late 4th Century (the last Hieroglyphic inscription is from 394). Hieratic Script, a cursive script developed alongside Hieroglyphics, was used from around 2650 BC to 300 CE. It was replaced by Demotic Script (700 BC-500 AD). Coptic had its own writing system derived from the Greek alphabet with some Egyptian additions.
Depending on how you define "ancient hieroglyphic language", it ended either with the end of spoken Middle Egyptian around 1300 BC or with the introduction of Egyptian Arabic around 700-900.
Coptic is a direct descendant of Ancient Egyptian. The only thing that changed is that they switched from Hieroglyphs to the Greek alphabet sometime in the 1st-3rd century. The switch happened because of Hellenistic influence, but also as a part of transition from the Ancient Egyptian religion to Christianity, where the old priestly class of ancient Egyptian religion literate in hierogpyphics and demotics declined and was replaced by Christian writers.