Ahhhhhh, more questions that I love. As I've said about airbrushes, there is so little information that is really useful for modelers out there about tools and mediums that we could use, it's silly.
regarding your questions, here's what I know: the gain color inks are similar to games workshop inks, or any other inks in that they are meant to tint the underlying base color when used in this fashion. Inks our water stand, and have a high density of pigment in them. Now, the Vallejo people don't say this, but I think they likely put some matte medium in their inks, because they draw a much more matte in other inks which dry shiny. You want to use water to cut it, to get rid of the density of pigment. You can mix it with their medium,but I found that the inclusion of some water is usually helpful to allow these things to flow well. If you are using other inks, you would use more of this type of medium and less water.
Vallejo model colors are great, but could stand a some thinning if you are to layer them very well. their paints are pigment in medium. A thin with water, various types of media, etc. They don't fit well with alcohol -- unless it is very dilute.
Vallejo game color line was actually developed (so legend tells) in order to make a bid to provide paint for games workshop. This is why their colors match the games workshop colors so much. They do have some great colors on their palette, but for very specific colors without having to do any mixing, model color works better.
Vallejo thinners= various kinds of media repackaged. Likely water + matte medium + flow enhancer + extender in some kind of recipe. I use airbrush thinners from Golden/liquitex, and they do about the same thing for much less money. You can also make your own -- use a matte medium for matte colors, gloss medium for gloss/metallics if you want them to shine.
Keep in mind Vallejo is an art company, just like Golden or liquitex. they are simply repackaging custom colors in smaller bottles in charging people a lot of money. There's nothing that special about their colors, onlythe method it that they are delivering them and how they are preparing them.
Hope this helps