Their damage reduction modification applies to all sources of % Damage and Explosion Damage, but does not apply to other sources like Melee and Ranged Damage.
When playing Renegade, Tier 1 items in the Shop and in Loot crates that you don't currently have a copy off will show up with Renegade's face next to it, indicating that you'll gain the +10% Damage (+2% after reduction).
Renegade's +2 projectiles is additive with other forms of multiple projectiles. So a Tier 1 Double Barrel Shotgun.png Double Barrel Shotgun will shoot 6 projectiles instead of 4, which is only a +50% increase in DPS, while other weapons go from 1 to 3 projectiles, increasing their DPS by +200%.