And according to physics, Earth orbits faster when it is nearer the sun than when it is farther. Does this, in any way, affect the length of day in the earth?
That is one of the effects that affect the lenght of the day as the duration between two difference passages of a certain meridian ( and not a 24 h day).
The other (stronger than the first) is the angle which the Sun crosses Earth in its journey north or south along the year. During equinoxes the Sun loses some time going a little north or south instead of going exactely west, while during solstices its path is exactely west gaining some time.
Both effects add resulting in what is called the equation of time:
If you took a picture of the Sun exactely at the same time of the day, you will see these effects as oscillations of the position of the Sun, producing a figure called analemma.
Analemma - Wikipedia, the free encyclopedia