I don't know the song, so I had a quick Youtube of the original. Funny thing is that I prefer the way you were singing it, over the original. But then the type of sound is not really my kind of thing. All that vocal fry in the original...I couldn't listen for more than 30 seconds. Kills it for me, but it makes it for others. I think that it has become fashionable to associate vocal fry with emotion.
Anyway, basic things... your pitch sounds good, and your phrasing fine. I do agree that it doesn't quite sound natural in parts. It sounds to me as if you were "finding" the accent. I wouldn't worry if your own accent comes through. If you adopt something of another accent, it shouldn't be so noticeable that that is what you are doing.
Stylistically, can't help you, bud. Not my kind of music, so I can't sense what may need doing for that.
But you do make it sound like you are into it. Singing because you like it is the best approach in my opinion.
I'd archive the clip, keep practising, and take a listen back in a year's time. You may be surprised how much else you've discovered since then. It can become quite addictive.