Congrats on giving such a tough vocal a shot, first of all, not to mention being willing to share it. I think you don't give yourself enough vocal credit: you clearly have the range to hit even the high notes. With some more control, I think you could improve on your performance. But that's the kind of thing that takes confidence, which takes practice and time. Stick to it. Singing, playing, recording: it's all great stuff, and I'm glad you're into it. Out of curiosity, what sort of studio does your friend have?
Um, that's basically everything I wanted to say. You have the range - the key to even better vocals is control. And as Luther said, it takes practice and time. But if you love singing, it won't be too hard!
...and you made me want to do the same thing (take the track+backing vocals and add mine). I might do it and post it if I'm satisfied with the result!