I think it looks very nice. I'm not sure how to help with backgrounds since it really depends on the program you're using and what you want to do.

For the background, I'd say reverse the colors so the bright part makes the shapes (unless you're going for dark magic, in which case you probably don't want the same dark color elsewhere) and put the bursts behind the character closer to where the power would come from - the horn or hooves or both. That way it looks like the magic has a source and is more obvious instead of just being passive things in the background... Make sense? With the way it looks subtly like fire at the top of the green, you could also get away with moving it down to "ground level" and making it look like the magic is coming up from the ground underneath her too. Hope that helps.