I assume "Muslim belief system" refers to Islam, the religion, not any specific social construct. There are a lot of inherent elements. One is monotheism: there is only 1 god. Another element is the 5 Pillars of Islam, which give guidance on how to live one's life. Hope this helps.
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Like the Associate Justices, the Chief Justice is appointed by the President and confirmed by the Senate. There is no requirement that the Chief Justice serve as an Associate Justice, but 5 of the 17 Chief Justices have served on the Court as Associate Justices prior to becoming Chief Justice.
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