Texture painting should work pretty much just like painting on a physical model. If you’re getting odd results in texture paint mode, there’s something wrong with your mesh object. It may have unapplied scaling or rotation, or you might be using the UV map incorrectly in some way. You should post a .blend file that demonstrates this brush-jumping behavior so we can diagnose the problem.
As for it not rendering, you need to create a material. All you’re doing in texture paint is creating an image texture that lines up with the UV coordinates of the mesh. Your material will have options for applying textures within it. Octane uses its own material system, as does Blender Internal, Cycles, and anything else. You’ll have to create an Octane material when the time comes, but image textures are just images no matter what the render engine. As I suggested earlier and justavisitor confirmed, you should be in Blender Internal when you’re creating textures, but once those images are all ready, you’ll do the rest in Octane.