This is a over and under express rifle, with spare shotgun barrels (probably 20 gauge or .410 considering the other barrels are rifled) that can be also mounted. The two triggers are for each barrel, unless there is actually only one barrel for each set (cant tell 100% from the angle) then it would be a kipplauf.
The rifled barrels feature leaf express sights and scope mounts for the included scope.
This gun is almost certainly built on order from a gunsmith, probably russian considering the location and the writing (maybe a gift?). The quality of the gun is fair but certainly not on par with expensive british guns, the wood is of poor quality (considering it is a custom gun) and so is the rubber pad on the stock (looks like something cheap you would find on a rem700 or weatherby). This is consistent with russian custom guns, they are rarely as elaborate as other western builds, much more practical and rustic.
This type of express,shotgun combination case is fairly common in europe among many custom gunsmiths, especially in the over and under type.
About the flintlock i couldn't tell you for sure, but it looks like it has a waterproof pan in the manton style, probably a sporting or hunting piece.