The answer to your first question is: sort of both.
The pistol in your main hand hits with weapon skill and your character's strength, the pistol in your offhand hits with ballistic skill and the strength of your weapon.
Skills which give bonus attacks from the Combat skill are melee attacks and use the main hand pistol and weapon skill. Skills which give extra attacks from the Shooting tree use the off hand pistol and ballistic skill. Skill which give bonus attacks from the Speed tree should specify if they are melee or ranged attacks in the description. But if I remember correctly, Quick Reactions and Lightning Reflexes use WS, and Ambush uses BS.