Is the apparent considered a matter of faith, such as with one who does not pray? And is such a one judged to be a disbeliever?

We judge based on outward appearance of faith, and it is not for us to search into what is hidden within. This is what the Messenger of Allah, peace be upon him, used to do with the hypocrites, and his rightly-guided caliphs after him. The Prophet, peace be upon him, said: "Whoever prays our prayer, faces our Qibla, and eats our slaughtered animal, that is the Muslim who has the covenant of Allah and the covenant of His Messenger, so do not betray Allah concerning His covenant." And Umar ibn al-Khattab, may Allah be pleased with him, said: "Indeed, some people were judged by revelation during the time of the Messenger of Allah, peace be upon him, and indeed revelation has ceased. We now judge you by what appears to us from your actions. So whoever shows us good, we trust him and bring him close, and we have nothing to do with his secret thoughts; Allah will judge him concerning his secret thoughts. And whoever shows us evil, we do not trust him nor do we believe him, even if he claims that his inner self is good." What is meant by outward appearance here is what manifests of faith with its conditions and pillars.