You know how when a battle starts up you have to listen to that little tune before you start? I hate that. I wish the battle just started immediately.
turn off music
Sound effects, actually, but you don’t really want to disable all sounds. I think it would be nice if there was no blocking sound effects, monoliths being particularly annoying.
Nice, I don’t know why I never thought of that. Still it would be nice if the sounds still played and just didn’t hold up the game.
Hi hydro & welcome to the forum. 
I’m not sure if you tried VCMI yet, but if I’m not mistaken, that battle intro is not even implemented yet. And I agree that after 10 years of playing Heroes, I am myself sometimes annoyed that I need to wait 5 more seconds in the beginning of every battle before I can make a move. So I believe we should keep this in mind as feature request for a later stage of the game. We’ll see if it’s easy for the devs to implement it as such that battles can start directly while the intro music is still playing. If not, then perhaps we could just have it as an option in the game settings to disable this intro.
EDIT: I have logged the request in Mantis.
Yes, that becomes a problem, especially with music turned off 
This option need to be included in future menu (which as yet was not planned, unfortunatelly).