AFAIK, the Church never persecuted anyone on account of a round Earth cosmology. Although different fathers thought differently on this matter, certainly by the time science began to emerge, there was widespread consensus as to the shape of the Earth. It is, however, a common misconception that people in the time of Columbus (for example) thought that the Earth was flat. But this misconception stems from a poem about Columbus written by Washington Irving in the 1800s.
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As per the OP:
It depends on what you mean by "God." Tolstoy treats "God" as "the infinite" to which a person relates himself. It is this "infinite" that a person uses as his basis for ethics. Certainly, this is not necessarily the personal God attested in most traditional Western monotheistic religions, even if it does share many of the properties. However, if I treat "God" in this way, I may become disillusioned by one particular god and move on to another, but I could never give up on God, conceptually, because I always need something to relate to, if I am going to make conscious decisions on how to behave.
If I understand what you mean, however, when you ask whether Christians have questioned the existence of God, or whether something could dissuade them from Him, then as to myself I would say yes. Ultimately, it is grace and peace through charity that persuade me, and if I were shown something greater (more "infinite" if you will), I would adopt that.
