Is Faustus presented as a traditional character that believes in God unquestionably or is he the manifestation of the Renaissance individual that was enquiring and questioning?

I think this was a bit of both. Faust would have believed in a Christian God with a healthy dose of superstition. Like the earlier play, Tamburlaine, Doctor Faustus is a play of deep questions concerning morality, religion, and man's relationship to both. England was a Protestant country since the time of Queen Elizabeth I's father, Henry VIII. Although theological and doctrinal differences existed between the Church of England and the Roman Catholic Church, the former still inherited a wealth of culture, thought and tradition from the latter. Christianity was a mix of divergent and often contradictory influences, including the religious traditions of the Near East, the heritage of classical Greco-Roman thought and institutions, mystery religions, and north European superstition and magic.