To answer your last question first:
No, That is not counter point. While It isnt impossible to play counter point as a solo musician, it would take a life time to master. The timber of any instrument would additionally render this type of practice asthetically worthless. Counter point is when two melodies are played at the same time. If you could imagine to different guitar solos being played at the same time, this is more like what counter point would sound like.
The style that you are describing sounds like she was playing a melody part in addition to a "mock bass line." Or alternatively, playing a lower melody while using the tremelo note as a tonal center to modulate over. This playing style has several names, depending on what musical style that you are playing. Music that uses an organ refers to this technique as "using a pedal point." Heavy metal, "droning." Theres a name for it in blues (which I can't remember.) I believe that they might call it droning on the sitar also. Jazz is almost technically defined by techniques which are founded on the same concept. I'm not sure what the technique is called in classical guitar, or flamenco guitar. Your gonna have to find out what the correct termonology is for yourself cuz if you use this **** that I just said, I'm sure you will fail.
To answer your first question:
It depends on what aspect you are describing.
A good idea might be to describe how the music made you feel, and how you think it was intended to make you feel.
You can describe the technical aspects, which is basically what you have been doing. Your description, however, would look more authoritative if you used the appropriate termanologies.
You could also describe the theoretical qualities of the music. Such as the chord names, scale names, harmonic structure, sectional arrangement, the compositional nature of the piece, melodic composition.
Going further into compositional principles, you could describe the historical relevence of either the techniques used, or the theory. Or to put it simply, this would be reference to the composers influences.
Another way to describe music is to actually describe it with adjectives the are used for the other senses (particularly sight.) Your teacher probabily will not be please with this, however, it is commonly how a producer will describe music. For example saying something like, "The tremelo picking had a fuzzy sound to it." Instead of saying that it was fast.
Bass guitar is the answer to everything