I have never used chrome vegtan leather, so I am affraid I can't help with that.
Dye - penetrates deep into the leather and gives a deep rich color
stain - sits on top of the leather and the color isn't as rich and full in my opinion
Acrylic paints are used to give solid(opaque) colors
Antiques - just fill crevices or low spots with dark color.
I don't think any of those edges are painted - at most they are dyed or stained
To prevent colors from bleeding or rubbing off on to skin, you need to apply a clear coat. Products like resolene, super sheen, tan kote all work for that.
Oil - used to preserve the leather or make it softer/more supple. I put it on before I apply finishes, and let it sit overnight so that it soaks evenly through the leather. Just a few light coats. You don't want to soak the leather with oil.
Leather straight from the tannery - colors will bleed when they get wet.
I do not know what brand of pens are available in your country. I buy my stuff from local office supply stores/art stores. They specifically say on the packaging that they are fade and UV resistant.
Both red weldwood ( original and gel) work great. The gel is not as messy to apply, in my opinion. It doesn't string out like hot cheese. The green can is water based, and I don't like it. Once the glues are dry, I can't forsee any problems.
Picture one might also be burnt with a heat gun to get that color too, but you can accomplish it with an air brush.