Hi and Happy April,
= = I'm no musician (and not much help elsewhere, some say), but I think you could improve the audio if the piano and voice were separated.
This might mean closing the lid of the piano and recording the music+ voice in one "take" then open the piano and do the video of the mechanism with a green-screen masking-off the player and vocal mic.
When combined you can mix the tracks, eg by having piano Left and vocal Right. . . . by copying you can adjust the response of L&R on different Timeline tracks . Have you added "echo" - I think it's just too much - but it could be the "brightness" of a large room.....always a problem in making recordings....with the lid-shut you can apply internal damping with a large carpet under the lid (take care), since you can adjust the brightness in Edit anyway, but IMHO you should try to achieve a "clean" (ie without reverb) with each take. The green-screen(see later), could be on one side of some thick carpet to help with the vocal-track.
As to visuals, I suggest you could use some cutaway shots, up to the point where you start to sing (thereby losing any sync-issues?); and maybe when there is music, without words. However, I think the bright wall behind the singer in black is a mistake, as it would be better if the background was a grey cloud-scape (ie no visual distration) and you (the singer, I assume) were dressed more like a Hollywood event,- but obviously you need to be comfortable with your outfit/image . . . . and it would be better if it was easier to see you - the most important part of any scene is a face . . . and that's too small, to see clearly. Hence my suggestion you include cutaways . . . but always from the same side, please. (Crossing the line). And get rid of the mic in front of yr face...and those mechanical supports.
*I noticed a "keyboard Cutaway" at 2min, but camera-angle is horizontal, so we can't "see" the individual notes being played, and that reflection that doesn't help. Also you need to experiment with manual focus, as the camera has fixated nearer the top octave... by raising the camera position (taller tripod?) this might help.
Lighting . . . It looks fairly well lit, probably because the room is white/bright, so maybe an out-of-sight flood to give some shadows would help cast some "shape" to the action - but don't overdo it. A light/shadow ratio of 4:1 might be too much . . . give it a try, after youve measured what it is now. If on a Budget, use 1 (or 2) halogen lamp on a floor-standing. Maybe as little as 100w (in a reflector) will do the trick...play with the colour balance - but keeping skin-tones correct.
Another technique that reduces the area of "Piano" in the scene would be to move the angle to a diagonal and Edit-in a Picture-in-Picture where the less interesting parts of the piano are . . . as the piano dominates the scene and there's a reflected image that makes no sense (to me).
?Cutaway1 is your face, expression to the song
?Cutaway2 is playing the keyboard*, for example if there is a Key-change...
So I think you need 3-takes with a single camera, positioned to the angles I've suggested.....but the benefit will be we can see the song building-up, the playing and the thro'-piano view presented.
+++It's up to you the way it's seen, by adjusting the views in Edit...
Is that any sense?
+Are the songs your composition?
& I did like the music.
+Goodluck