The multiplier from any sneak attack is only applied to the base damage of the weapon. Any bonuses from perks, potions, enchantments etc... are applied AFTER this. This is true whether you are talking about the automatic 2x sneak damage, or any of the perks that increase it.
Yes, they will affect the damage. Sneaking does not change what type of attack it is. if you use a 1h weapon, anything that increases 1h damage will still apply.