Can Rayleigh scattering explain the orange color of the Titan sky? It is my understanding that Rayleigh scattering depends on both the length of the particle as well as the wavelength. Due to the similar lengths of molecular nitrogen and oxygen it is blue light that gets scattered down to Earth giving the terrestrial sky its blue color. But what about Titan? The Titanian atmosphere has a vastly different chemical composition than Earth(on Titan it is mostly nitrogen dioxide and methane). So is there evidence that Nitrogen Dioxide and Methane tend to scatter longer wavelengths than molecular nitrogen and oxygen do? Hence why extraterrestrial skies are not always blue like Earths.
 A: The blue sky on Earth is because of Rayleigh scattering, and because the particles in the air scatter blue light more then red.
This is the Tyndall effect, he discovered that when light passes through a fluid with particles in suspension, blue light is scattered more then red.
The amount of light scattered is inversely proportional to the fourth power of the wavelength. 
This works if the particles are small. Much smaller then the wavelength.
The sky on titan is blue. 
Please see here:
https://lightsinthedark.com/2011/12/18/the-colors-of-titans-sky/
You are right, that the size of the particles in the atmosphere does decide the color of the sky, because with larger particles, Rayleigh scattering is not dominant, but Mie scattering is.

On Mars, Rayleigh scattering is usually a very weak effect; the red color of the sky is caused by the presence of iron(III) oxide in the airborne dust particles. These particles are larger in size than gas molecules, so most of the light is scattered by Mie scattering. Dust absorbs blue light and scatters longer wavelengths (red, orange, yellow).

A: The atmosphere of Titan is 95% nitrogen and 5% methane. There is nothing vastly different about the size of those particles in the atmosphere compared with Earth. However, there are large molecules - tholins - that are synthesized in the upper atmosphere and "rain down" on the surface.
A significant difference with the Earth is the density of the atmosphere. The atmospheric pressure at the surface is about 1.5 atmospheres, but since the temperature on Titan is much lower than Earth, the density is about 4 times higher.
The optical depth to Rayleigh scattering of blue light is somewhat less than the optical depth of the Earth's atmosphere when looking straight up. That means most blue light (and light of longer wavelengths) makes it to the ground from the Sun when it is high in the sky.
When the Sun is lower and the direct light must pass through a larger optical depth, we see that blue light is scattered out of the beam and we get red sunlight.
On Titan the optical depth of the atmosphere is sufficient to scatter a significant fraction of blue light out of the beam even when the Sun is at zenith.
There are then additional complications in that methane will tend to absorb the red part of the spectrum and the tholins form a thick haze in the upper atmosphere with an orangeish colour. You also have to account for multiple scattering.
I don't think there is a single answer. With Rayleigh scattering you might expect a reddish sky towards the Sun, but to recover a bluer sky through multiple scattering at large angles from the Sun. But absorption by methane and the tholin haze are extremely important, as can be judged by the fact that the surface can't be seen in visible light from space.
