What are the exact causes that differences in sunrises are shorter around june and december but long in march and september?
If I understand you correctly, you ask why does the length of the day not change much around the winter solstice.

There is no mystery here: The rate of change of day length has (almost) nothing to do with the elliptical orbit of the Earth. 

In autumn the days get shorter; the rate of change of day length is negative. In spring the days get longer; the rate of change is positive. 
At midwinter solstice the rate of change of day length is zero: The length of the day doesn't change.  Exactly the same is true in midsummer. Mathematicians would say that the "day length function" is stationary on those dates.

This has nothing to do with the elliptical orbit. Every smooth function is stationary at its maxima and minima. The reason is not astronomical but mathematical.

Note that the Earth is furthest from the sun (and therefore moving slowest) on July 4th.