A couple coats of oil and the stock will be sealed , depending on the oil of course .
Oils like linseed can take more . White tung I normally do 7-10 coats , not because that’s whats needed to seal the stock . Its more to create the finish im wanting .
As to your barrel .I would recommend installing the sights first . Then remove them and brown the barrel . Then replace the sight .
If you try and install after you have browned the barrel you take a good chance of messing up the browning while cutting the dovetails .
With your lock . If your going to grey the lock , then you will need to file and sand the outside of the lock plate . If you Brown , then boil , you will convert the red iron oxide to black iron oxide. In other words if the whole lock plate is brown . When you boil it , the whole lock plate will turn black . If you card the rust back to only a very light covering . You will then have a light covering of black in the areas you left the brown rust .
If your wanting the French grey or a more grey used look I would recommend a different process .
a) you can use a cold blue . Blue the plate , then using steal wool , rubb the blue back tell you get the grey your looking for
b) Navel Jelly spread on the plate will give a grey discoloration. It can be used by itself or to remove the cold blue
c) a strong vinegar solution like ,white vinegar , yellow mustard , let on the lock , will form what call stain rust , which will stain the metal into a pattern or grey patina of sorts
