Nice little lockset , talesof .
These were fairly heavy-duty units , designed to be disassembled & cleaned easily .
I wouldn't be bashful about taking it apart to clean & lube it .... very few moving parts & springs , compared to modern assemblies .
I'd also add that they were designed with a bit of 'slop' so that it would be unusual for the lock or passage section to jam .
These little guys typically get a build-up of fine metal 'dust' , from metal-to-metal contact during use (brass , steel & iron) .
I still see strike-plates for these available (old ones , that is) at various 'sales' around everywhere for a buck or two .
It might be possible that the escushion plates & doorknobs came from another set , since the skeleton-key hole is not in 'exact' alignment with the lockset assembly .
Skeleton keys are fairly simple to make/cut & I bet you could make one (by filing down/cutting/grinding) from an existing skeleton key .
I know you gots skills !
One issue with this type of lock is the depth of the mortise needed to fit the lock into the door (modern-ish doors [such as hollow-core ones] often don't have enough 'meat' [wood] to fully mortise the lock mechanism) ; if a modern door-install is the only option , it's wise to give the mortise a brush-coat of Elmers wood glue - in the event that the core of the door uses 'chipboard' construction -(this prevents little bits of the chip-wood from entering the mechanism & making it jam) .