Treehouse offers a lot of useful information and courses. I would recommend it. After finishing the Treehouse courses you are interested in, I'd suggest moving on to Code School.
I have no idea what the symbol is supposed to represent. That is one thing you could work on. Make the message clear. Refine the edges. Preferably turn it into a vector.
Self taught. I tried a course on media design about three years after I had started designing, but I did not feel like I was learning a lot, so I quit the course.
I cannot paint nor draw or whatsoever and to be honest, you do not need those qualities to be a graphic designer. I have never had any complications because I am not an artist.