Regarding Our Lady of Fatima, and the Miracle of the Sun, I have to wonder if maybe a flat earth model fits better with the circuмstances of the Miracle of the Sun.
According to those many faithful who were at the Cova, they observed that the sun appeared to be hurling at them, and they were afraid that it was going to fall to earth. In a flat earth model (if I'm recalling correctly) the sun is closer to the earth in proximity.
However, if the sun is as far away as a ball-earth theory supposes, then I think that it would be difficult to have the same effect of the appearance of coming so close to earth, and the temperature rising, and everything in the vicinity drying out suddenly after it rained. I could be wrong.