If i see a supermutant far off and wanto snipe his head off with a rifle, does perception affect this is any way?
Does having a higher skill affect the damage?

All that Perception affects in that case is how close you have to be to that super mutant before his red tick appears on your compass. The stat that affects your Guns skill directly is Agility.

The higher your Guns skill, the more damage you'll do, and the more likely you'll be to get a hit.

Thanks.

Like Gator said - it only impacts how soon things appear on the compass. However a certain companion, available almost from the start will give you an effective perception of 10 for the compass pickup. So it is basically worthless for a sniper. Except to qualify for perks.

doesn't the distance from which you'll be able to see someone that the certain companion gives you stack with the perception of the player?

I could be wrong but I think he just bumps your Perception to as if it were 10 when it comes to the compass.

I was worried on my first play-through... when you first select your SPECIAL,
under Perception it does mention Accuracy - but it doesn't actually affect accuracy. I Hope.

Actually they don't stack, but it does allow you to use his perception stat for compass readings.
The wiki says his Perception is 15