Using Stellarium (or a comparable sky mapping resource), what is the phase of the Moon on October 5th, 2018, at 1:30:00 as seen from Arlington and, using the Illumination-Position map, how many degrees through its orbit is the Moon, in degrees?

The Phase of the moon on October 5th, 2018 was Third Quarter Moon (Waning Gibbous Moon).

It's degrees through the orbit was 16.21 degrees North.

Explanation:

Illumination is 19%

Distance 366 619km

The moon's various phases are caused by the angle from which an observer on earth sees the moon illuminated by the sun as it orbits round the planet.

As the moon orbits round the earth one can see various fractions of its surface reflecting sunlight as he/she looks up in the sky.  

a is the answer i believe.