Well, not only breathy and shaky but also not in tune. Suggest you get a few professional singing lessons. You can learn this like you can learn guitar - only a few bast***s are naturally good at it.
Alright, first- practice your lung capacity and breathe control. A great exercise for this is to slowly take in air through your mouth, until you can't possibly take any more in. Then, quickly inhale a burst of air through your nose, you should be able to pull at least a little more in. Then, slowly release all of the air through mouth like you're breathing it out of a straw.

To help with pitch, sing to scales you play on an instrument (make sure this thing is tuned verrry well). For example, if you're singing a song in the key of C major, find a C note on the guitar and sing to the note until you hear an "octave" effect, or hear that you've matched the note as closely as your ear notices. It might take a second to find it with your voice, but when you do, hold onto it for dear life until you're out of breath. Then go up one more note on the scale to D, repeat, go to E, repeat, etc.
I haven't had a chance to hear the audio, but just from the words breathy and shaky I know what to recommend: study proper breath support (preferably with a teacher, if at all possible). This will reduce those problems and will also help with pitch issues.
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The Byzantine scale was useful until the Ottoman scale came around and totally annihilated it.