I would like to know if the height and dominant foot of the players have any influence on the game, or is it just an aesthetic detail without function?

Good question. I think it have affect, but ofcourse dont know how and what.

the height have Anyway impact on speed and heading

If I remember right, short players do better in offence while tall ones perform better in defence. With dominant feet it's more complicated, for long shots it's better for a player to play on the same side of the pitch as his dominant foot while for passing (cross to box iirc) it's the opposite. Again not 100% sure, it's been a while.