Thanks for your reply. I actually am a fan of Stephane Grappelli. I have of few recording of him and Djangle Reinhardt playing, and I must say I love those very much. Though I was inspired to write this after hearing Ian Cooper play Dark Eyes from Hell Raising Jazz.
As for the violin part, I do agree with you about it being too simplistic. I know I can make it better, since my main instrument is the violin, and that's the only instrument I'm actually good at playing. I'll eventually add some double stops and maybe implement some of the virtuoso techniques by Paganini, and the others like him, like left-hand pizzicato and such. Triplets, arpeggios, and there are many others things I want to put into the piece eventually, though I want it to start off simple, and then get more and more complex and detailed.
I'll definitely have to look up some information on Jazz harmony and the other things you mentioned, because as I said before, this really is my first attempt at creating anything musical.
I'll work some more on it, and I'll do a little research, and then I'll post what ever changes I'll have made.