Modern suppressors allow the use of full-power ammunition, do not reduce the muzzle velocity, do not contact the bullet during flight, and often aid accuracy.

Do suppressors increase range?

No. Suppressors don't increase velocity as the bullet isn't "sealed" like in a barrel.

Does a suppressor reduce damage?

In short form: Silencers reduce the push the bullet gets from the expanding gas. This reduces it's velocity, and the velocity of the bullet directly effects the damage the bullet will make on target.