Im completely new to knives and knife sharpening. Please excuse me if some of these questions have been asked a million times. Ive got a few questions, so please bare with me.
1. What's the best way to sharpen a convex knife?
I think the easiest way to sharpen convex, is sandpaper on a forgiving backing, like leather, using a stropping (edge-trailing) stroke. This is my favorite method, in fact.
2. Should I sharpen a convex edge on a stone?
Whether you should or not, is pretty much your preference. You can, but if you're trying to maintain the convex shape, it can be a little more challenging on a hard stone. It's very simple, however, to just micro-bevel the very edge of any knife (convex or not) on a stone.
3. When should I use a stone and when should I use a leather strop?
Using a strop, lightly and frequently (before the edge is allowed to get too dull), is the best way to maintain an edge. If used with compound, the choice of the compound can also add versatility to stropping. Finer compounds for light maintenance & polishing, and coarser compounds for restoring or maintaining some 'bite' in the edge. Go back to a stone only if/when stropping can't quite fully restore the edge.
You can also 'strop' on sandpaper (wet/dry silicon carbide type), and the grit selection can be tailored to the needs of your edge. Something like 400-800 grit for a 'satin' finish and somewhat toothy edge, and 1000+ grit for a higher polish. Follow that with stropping on bare leather, or leather with green compound, to clean up burrs on the edge. This is how I've been maintaining most of my edges lately.
4. I've got red, white, green, and black polishing compound/rouge. In what order do I use them?
As mentioned earlier, the sequence would usually be black --> white --> green, then the red might (or might not) help clean up & polish a bit, depending upon the steel type. I'd ordinarily stop at the green.
5. How often do I oil a knife?
Focus on keeping the knife clean first. Then, a minimal amount of oil will usually be fine, applied only as needed. Don't oil a dirty knife, as it will just gum up the joints.
6. Is a 1k/6k Stone too much of a drastic jump?
Not necessarily. If it's producing an edge that works for you, that's all that matters.