Here you can see in the first bar the reduction of the first bar has the ^1 on the second beat while in bar 2 the two tones are stemmed together. Why?
The reduction is illustrating that the melody notes serve multiple conceptual functions.
The initial C, according to this interpretation, is heard as a separate, bass voice that carries through the first three measures. The upper voice begins on F, then moves to E and G, then just G. The reason the E and G are written simultaneously is to show that that voice functions chordally even though the actually pitches are song one after the other.
Measures 4 and 5 are being interpreted as a single "voice" that forms a chord.
In measure 6, the interpretation is that there is now a return to two voices, with the D being dropped an octave in the reduction to show its function as the harmonic foundation (i.e., bass voice). Measure 7 is similar, but without the need for an octave displacement.
In measure 8, the parenthetical note is there, because while it's not a heard pitch, it is "conceptually heard" as forming a major chord for the ending. This can be demonstrated by playing the melody and actually playing the A at the end along with the F. It will sound "right"; whereas playing some other note that forms a different chord with the F (Ab or D, say) will clearly sound wrong.