Neotonal Lied (without words) or Romance in C Minor

Hello everyone,

I’m working on a new piece that’s more harmonically adventurous than my usual style and would love your feedback. It was originally for flute and piano, but since I did not like the flute sound from Musescore, I used a soprano voice instead. That made me consider turning it into a Lied with syllables rather than lyrics (since I can’t write lyrics).

The main theme began as a neotonal composition practice exercise based on a post in the Talkclassical forum:
    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 [:A:][:BA:].

I’m unsure about a few things:

• Does the piece and structure work overall? Does the harmony work? (I am still considering piano voicings in section B, particularly in m.10, but A is finished).
• Since A repeats four times (and it is a period, so there is internal repetition too).
  Should I get rid of the initial repetition of A? Or maybe varying the harmony/accompaniment in the second repetition or even adding a C section?
  I always get stuck with same simple form and I also do not know how to reharmonize themes without making it lose the balance. 
• Does it work better as a vocal piece or another instrument would be better (specially since there are no lyrics)?
  Not sure if it should be a Lied, a Song without words, a Romance, or what.
  Is there a way to indicate that the melody can be played with any suitable instrument freely?
• 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? 

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.