Pedant alert:

In the opening post:

Due to the eliptical nature of Earth's orbit about the Sun, ...

The ellipsicity to the orbit has at best an extremely minor bearing on the solstice/equinox occurances. These would occur even if the earth's orbit around the sun was a "perfect circle."

It's the inclination of the earth's axis of rotation relative to the perpendicular to the plane of the orbit that produces these effects.

The winter solstice, in the Northern Hemisphere, when things are "coldest" actually occurs very nearly at the point where the earth is closest to the sun, IIRC, so the "elliptic factor," if significant at all, should make things warmer, when the inclination is making them colder up north.

And later:

It is the extra speed we have around this time that starts to make the sunset later while the days continue to shorten

A somewhat dubious assertion requiring the "how do you define se ... "speed" question.

The observation that the earliest/latest sunrise is at a different time ("in" a different day) than the latest/earliest sunset, and neither is "in the same day as" the solstice/equinox is largely a matter of geometry. Easily observed but exceedingly difficult to "explain" with simple math, hence a visit to a planetarium with models is the best approach to at least an intuitive grasp of it all.

John