1. No, its a musket with the battered quality. All the archetype does is eliminate your option to select a pistol or blunderbuss.
2. No. Early firearms explicitly state that you must reload each barrel individually. This remains true whether its a one handed firearm or two.
3. I don't see a question here.
4. In general if it says muskets it means musket in the same way longswords refers to a longsword. ie rapid reload (muskets) is different and non-inclusive of rapid reload (double-barrel muskets). If they want to be inclusive of all types of two-weapon firearms they will state such. Or if a particular weapon should benefit from abilities of a similar weapon (like longbows and composite longbows) it would state such in the weapon description.
I doubt you see a PFS specific ruling as this doesn't appear to a be a society specific question rather they appear to be general questions about game rules.