How can one use theory/harmony in order to learn BWV anh 114? I am only talking about theory/harmony in order to be able to play and memorize this piece.
The way I use theory/harmony to memorize a piece is that I will remember the chord progressions. Instead of thinking something like
So the left hand has
B G D Gand the right
D C Dand then moving to the next set of notes
using theory I can easily think
This is a G major chord in first inversion and then it goes to a C major chord etc
and after that, using harmony I can think
This piece starts off in the G major scale. It goes I,IV,V,vi etc..
But you'll still have to remember the voicings of the chords. In the Minuet you mentioned, Bach doesn't have full chords in the whole piece, so you can use theory/harmony to remember that he plays the root of the chord on one bar, the 3rd on the next bar etc..
Similarly you can work your way for the melody of the right hand. The melody starts off with the 5th and then jumps down to the root and moves in steps all the way up to the 5th again
Same as a lot of pieces. Take one bar at a time, and work out what the harmony/chord is for it. First two bars are g major. So the main notes in them will be G, B and/or D. Then look at which inversion is used. It won't always work, but it's a method I get students to use when sight-reading ; before playing, work out a map of what's happening. Is the cadence a perfect or an interrupted, for example.
I think so.
I particular piece uses many subtle variations with repeated phrases. Knowing the theory of those subtle changes are about can help with memorizing. For example...
...harmonically this is just a descending bass from scale degree
^1 with the treble part making two essential motions
...when it's repeated here harmonically nothing really changes in terms of the bass and treble outline. Actually, the treble is exactly the same.
Knowing the harmonically essential structure can help reveal patterns which aids in memorization, but also it provides information for performance where you might articulate those essential notes in some way to emphasize them.