Romance Vocalise in C Minor for Soprano and Piano

Hello everyone,

I posted this piece on the "work in progress section" but after modifying a little bit the form and cleaning it up I felt it was in an advanced state for being there (moderators, please, if possible, delete the other post as it seems I cannot delete it myself. Sorry about the trouble).

I composed this inspired by a composition practice exercise based on a post in the Talkclassical forum for writing some neotonal music (Bartok, Stravinsky, etc):
    Step 1. Write a diatonic melody in a mode missing one note.
    Step 2. Use a different mode or scale for the harmony.

My melody is in C Ionian without F, and the harmony is C ascending melodic minor (C major with Eb, though I ended up using E here and there too).
I later added a B section with the melody focusing on the unused note F.
The form is ABA'BA.
A' is exactly same melody and accompaniment type but with different harmonies, specially in the first chord, that is Major instead of minor. 

Some of my concerns are:

• Does the piece and structure work overall? There is lots of repetition but I feel that having the harmony of A' changed helps on the overall flow. 
  If the structure is repetitive, how could I add variation? I am considering changing the second B for a different theme (C) but I did not manage. 
• Does the harmony work in general? (There might be some weird spots, specially in section B).
• Does it work well as a vocal piece or another instrument would be better (specially since there are no lyrics)?
• Technically it is in C Minor (it starts and ends in it) but since it uses mostly natural A and natural B throughout, and natural E on the melody, I used the Cmaj key signature. Is that okay or I should change it to using three flats like in natural C minor? 
• I am not sure how to notate the piano sections that consist of ascending chordal accompaniment (with the pedal, although it is not marked). Is there any obvious mistake in the notation?)

Thanks for listening and any feedback is welcome!

PD: I found out that the first 4 notes and main motive of the piece (and the mood, because of the vocal singer) is similar to Jerry Goldsmith's theme to 'The Illustrated Man'. I never heard it before so it was a pure coincidence. I think the harmonization of those 4 notes is different, though.