Hello,
is there any option to reduce the players voice (especially during fighting)? Or maybe a consolecommand that i could use? Thanks for your help in advance!

Not that I am aware of, turn down your sound?

It's not ok to turn down all sounds, I hate my character's grunts but I want to keep everything else...

I also notice some high sound, especially on magic. In that case it's slightly reduced while playing in 3rd person, though I'm not sure if the same occurs with character voices.

Unpack the voice.bsa or whatever, find the offending voice files and write down their names. Take a blank sound file of the same type and make copies, renaming them to match the player voice files.