Caro thereminista Italiano,
First of all, we shall take a moment to reflect on the fact that the theremin is the most difficult instrument ever invented. If I may quote the late Clara Rockmore, "It is much more difficult than the violin, which I played for years".
Let us begin with your first note.
You are playing this piece in the key of C minor, which means that your first note is a G. Unfortunately, your first note was not a G, it was closer to a G#. This threw you off, so your second note, C, was flat. Playing the theremin is a bit like a race. If you stumble at the starting line, there is a good chance you will never recover and it will screw up your entire performance.
You have made your task more difficult by playing "a cappella". Amethyste is right, if you use some kind of accompaniment, your timing and pitch will be much better because you will have a constant reference to keep you on track. DON'T PLAY ALONG WITH A FINISHED PERFORMANCE. Use a recording specifically made for accompaniment. Since you are a trained classical pianist, I presume you are in a position to provide your own.
I strongly recommend that you start using an audio pitch preview. This way, you always know that your starting note is correct. The advantages of a pitch preview for a serious, precision thereminist cannot be overestimated.
I have heard some of the practice tapes that pianist Nadia Reisenberg made for her sister Clara Rockmore, and in many of them, waaaaay in the background, you can hear Clara singing along "sotto voce" with the piano. She did this so that the phrasing would be exactly right.
It is essential to know the correct notes and exact values of those notes if you want to play a piece like APRES UN REVE at the professional level. Are you able to hear this song correctly from beginning to end in your musical imagination? You only played fourteen bars of it (which you then partially repeated an octave higher) but some of the notes were wrong so I was unsure whether you knew what the right ones were.
You mentioned that one of your concerns is phrasing (fraseggio). In a work like this, phrasing is EVERYTHING. I think the problem here is that your playing is not sufficiently advanced to allow you to think about phrasing because you are so concentrated on the basics of simply getting the notes right. Phrasing comes when technique is no longer an obstacle.
Later on this morning I will make a quickie recording "a cappella" of the section of the Fauré that you posted to Sound Cloud so you can hear how I think it should be played. Perhaps it will be a help. If not, beam it into oblivion!
As I said at the start of this thread, it is very difficult to make any constructive suggestions about someone's theremin technique when you can't see what the person is doing. If you could post an unlisted video to YouTube that shows only your hands, and using an alias, no one would have to know that your real name is Silvio Berlusconi.