Welcome on your first posting Mr. Polecat, and congratulations on your new/old American Drilling. I never owned one of these guns, but I believe I can answer at least some of your questions:
1) The U.S. never had an official proof house as England and many European countries did. Some manufacturers here did their own in-house proof testing and stamped their guns with some mark to indicate they passed. Others did not. Your best option is probably an inspection by a competent gunsmith who specializes in doubles or drillings.
2) See no. (1) above.
3) See no. (1) above.
4) I would not automatically assume anything. including chamber length. When you have your gun inspected by a competent gunsmith, ask him to measure the chambers if you do not know how to do that yourself. Then you would want to use the appropriate low pressure and lower velocity ammo suitable for a 100 year old gun in order to prevent damaging the wood, breeching surfaces, and yourself, of course.
5) I myself would never recommend drilling and tapping the rib for any sort of scope mounting on this drilling. You paid up for this gun because it is a low production collectible vintage piece. Unless you wish to immediately lose hundreds of dollars in value by drilling a few small holes, you would do best to stick with your Valmet combination guns when you wish to use a scope.
6) Same as above. Unless your gun is quite abused and in desperate need of restoration to salvage and preserve it, any unnecessary refinishing is more likely to reduce its' value rather than enhance it. It may look prettier, but it will likely be worth much less to any collector. if you did decide to reblue the barrels, only slow rust bluing would be appropriate. Hot salts bluing should never be done on a gun with soldered ribs, as the salts will attack and loosen the solder. You'd be looking at around $300.00 for a decent slow rust bluing job, perhaps a bit more considering the extra work with the open sights versus a shotgun with only a bead.
7) I have purchased a couple doubles from Jerry Andrews in Moundsville, West Virginia, and have heard from numerous sources that he is a knowledgeable, competent, and fair priced double gunsmith. You might want to check him out and give him a call since he is relatively close to you. There are a couple guys on this site who collect these American drillings and will hopefully have more information to give to you concerning proper loads and the best choices for gunsmiths. I'm betting that none of them is going to encourage you to start drilling and tapping holes in one of these guns. Looking forward to seeing your pics when it arrives.
