Lethe (Vocal Cover)

If you aren't interested in doing clean vocals, as somebody who is just starting out you should really try to find a type of growl or scream more comfortable on your own vocal chords. It sounds like you are forcing it and won't be doing your vocal chords favors in the long run. It is okay to do a vocal cover in a different vocal style than the original.

The second main thing is that you may want to turn down the vox more so that you aren't listening for the lead and stay with the rhythm instead of behind it. If you love it keep at it.
It doesn't hurt, and I'm learning about a year and half right now. But only now I bought a microphone, and started to record, listen, analyse how do I do it and trying to make it better. At first I didn't wanted to do cleans at all, but thought I could try to put some scream with the clean voice. The sound was "interesting" (for me) and I decided to leave it in track. About the second thing, I didn't understand, you are talking about my vocal, or is it in the song vox? Thanks for comment!
The good thing about starting to record is that you will start to hear back your own voice how it sounds to others. Make sure you take advantage of that so you can make adjustments to your vocal technique. To me, it sounds like your voice type would be better suited for a slightly lower growl than you are doing. The reality is that harsh vocals will almost always do some degree of damage. The point is to minimize it and be smart about it.

The second point was a reference to the original vocals. I'm not sure if Stanne's voice sounded somewhat low because you tinkered with the mixing of the channels or because the volume was just much lower on the track than your recording. But, you can use many different methods to either completely lift the vocals or to greatly reduce how loud they are. The degree that you can create a karaoke track depends on the original mixing. Anyhow, one problem that can come from singing to music with vocals already in them is that it is much easier to follow their voice and end up being off beat or lagging behind. You'll notice in some sections that ended up happening. Sorry for the long explanation. And good luck.
Thanks for good explanation!) Yeah I noticed that I sometime go off the beat, and I tried to reduce vocals, though it didn't gave any results. Again thanks for comments, I'll practice more.)