JDW and OB are right on. I am also a hobbyist and do my own barrels. They look good and professional:Below are my comments:
1.polishing,what grit is best- I use 220 if the bbls are slightly rough and then finish with 320.

2.solution. I use Baker's Modified per the Baker Gunsmithing book

3.Should you use a hot box.No- I get good rusting without it.
4.application. Small foam brush

6.Carding.Fine steel Wool
7.Number of coats.8-10 Usually
8.oiling. Neutralize with Baking soda in water and then I use G96, or something similar