I never asserted either of the two issues you listed.If the sun is wobbling about on its axis, there must be some force at work. What is it? And, even if it was wobbling about on its axis, that still wouldn't account for the seasons, because the sun has spherical symmetry.
One other thing: It is not the Earth's distance form the sun which accounts for the seasons. During the northern hemisphere's summer, the Earth is actually at its furthest remove from the sun - about 94.5 million miles. What accounts for the seasons is the angle at which the sun's radiation hits the earth, and the consequent size of the area over which a given amount of radiation is spread.
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