Nope- assume nothing, ask all the questions you have.
1. On the tight fitting plug. I assume you mean at the end of the barrel. You'll need to whittle that out of some soft wood and the way I do it- that plug becomes very important because it does double duty. Not only does it keep the solution out of the bore- it also serves as a handle for holding the barrel. I hammer the plug into the bore so it fits tight. I tap, not pound.
2. On the sights, leave them off while you brown the barrel so you can get a nice even swipe of solution along the flat. NOW a lot of nice browning jobs get marred afterwards while driving in the sights. You need a brass drift and the easiest thing is a brass bolt with a hex head. File down the hex until it matches the dovetail slot in the barrel- then you have a good drift to drive in the sight afterwards. Be very careful because if the drift slips off it will scratch your browning job. You might want to put some card board shields around the area.
3. "Final Finish" after 5 or6 coats, depending on the humidity in your area, you are pretty much done. What you have may not look like what you wanted. Applying Linseed Oil OR beeswax will "even out" and smooth/shine the finish and make it look better. You do this after the soda wash which neutralizes the rusting chemicals.
What should you use, Linseed Oil or Beeswax? Folks differ on this so try a little of both on the bottom flat that is hidden by the forestock. Decide which of the two you prefer.
4. Shower? I made a wood cabinet with a heat lamp and a towel rack (damp towel) because I do a lot of browning- I further lock in humidity with a plastic leaf bag over the box. Recently I realized I was overdoing it, the barrels brown well just resting them against a wall.
If you have low humidity think about some sort of box. A cardboard box would probably work fine, Set the barrel against one side and maybe put a damp rag in a pie plate on the bottom- away from the barrel.
The first coat or two won't be even, that's when a lot of folks panic and try to go back and forth with the solution, covering every spot. Remember, just make one long, slow swipe per flat and if you didn't get every spot don't worry, you'll get it on the next application.
On the carding, with LMF you just use hot water (distilled) and a terry cloth rag. You really should not have loose rust- removing loose rust is the purpose of carding. Don't fret on this, wipe it down with a couple of strokes of the terry cloth and you're done.
If anything is not clear- keep asking more questions.
