The answer to the first question is yes. Although days will remain 12 hours long at the equator, the sun will be lower in the sky all day long at the solstices.
I will be glad to critique your thoughts for the second question.
if the tilt of the earth's axis was increased beyond 23.5 degrees, will it cause seasonal variation in the equator to decrease?
if the earth's axis becomes perpendicular to the orbital plane between the earth and the sun will it increase the length of night, increase in the length of year, eliminate seasonal variation or eliminate tides?
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